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implicit derivative (dy)/(dx),-x+y-x^3=y^3+4x^2
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implicit\:derivative\:\frac{dy}{dx},-x+y-x^{3}=y^{3}+4x^{2}
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integral of ((x+1)^2)/(x^2)
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\int\:\frac{(x+1)^{2}}{x^{2}}dx
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integral of 1/(n(n+1))
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\int\:\frac{1}{n(n+1)}
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integral from 0 to 1 of integral from x to 1 of 6*x/y
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\int_{\:0}^{1}\int_{x}^{1}6\cdot\:\frac{x}{y}dydx
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limit as x approaching 3+of (6-2x)/(|x^2-3x|)
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\lim_{x\to\:3+}(\frac{6-2x}{|x^{2}-3x|})
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y^{\prime \prime}-3y^{\prime}-18y=0
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y^{\prime\:\prime\:}-3y^{\prime\:}-18y=0
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area x^3-15x^2+50x,-x^3+15x^2-50x
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area\:x^{3}-15x^{2}+50x,-x^{3}+15x^{2}-50x
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limit as x approaching infinity of e^{x+2}-4
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\lim_{x\to\:\infty\:}(e^{x+2}-4)
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sum from n=0 to infinity of 1/(2n+3)
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\sum_{n=0}^{\infty\:}\frac{1}{2n+3}
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-2y^{\prime}+6x^2=0
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-2y^{\prime\:}+6x^{2}=0
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integral of (-x^2+x+4)/(x(x-2)^2)
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\int\:\frac{-x^{2}+x+4}{x(x-2)^{2}}dx
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integral from 0 to 1 of (3e^x)-(3xe^{x^2})
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\int_{\:0}^{1}(3e^{x})-(3xe^{x^{2}})dx
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limit as x approaching 6 of (x^2-11x+30)/(x-6)
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\lim_{x\to\:6}(\frac{x^{2}-11x+30}{x-6})
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sum from n=1 to infinity of ln((n+1)/n)
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\sum_{n=1}^{\infty\:}\ln(\frac{n+1}{n})
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limit as x approaching-infinity of+infinity-infinity
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\lim_{x\to\:-\infty\:}(+\infty\:-\infty\:)
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limit as x approaching 0 of (sin(8x))/(9x)
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\lim_{x\to\:0}(\frac{\sin(8x)}{9x})
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limit as x approaching infinity of 8ncos(9nπ)
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\lim_{x\to\:\infty\:}(8n\cos(9nπ))
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integral from 5 to 6 of pi(-x^2+11x-30)^2
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\int_{\:5}^{6}\pi(-x^{2}+11x-30)^{2}dx
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9y^{\prime \prime}-y=xex/3
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9y^{\prime\:\prime\:}-y=xex/3
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integral of (x^3-4/(\sqrt[3]{x)}+9/x+6e^x)
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\int\:(x^{3}-\frac{4}{\sqrt[3]{x}}+\frac{9}{x}+6e^{x})dx
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integral from 1 to 2 of integral from 1 to 4 of xy+1/(y+1)
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\int_{\:1}^{2}\int_{1}^{4}xy+\frac{1}{y+1}dxdy
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integral of sin(x)x
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\int\:\sin(x)xdx
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integral from 3 to 8 of x^3ln(3x)
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\int_{\:3}^{8}x^{3}\ln(3x)dx
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y^{\prime \prime}-8y^{\prime}+20y=200x^2-39xe^x
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y^{\prime\:\prime\:}-8y^{\prime\:}+20y=200x^{2}-39xe^{x}
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integral from 0 to 8 of xe^{-x}
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\int_{\:0}^{8}xe^{-x}dx
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derivative of-x/(x^2+y^2)
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\frac{d}{dx}(-\frac{x}{x^{2}+y^{2}})
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integral of x^2sqrt(ax^3-b)
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\int\:x^{2}\sqrt{ax^{3}-b}dx
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limit as x approaching 6 of cos(1/(x-6))
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\lim_{x\to\:6}(\cos(\frac{1}{x-6}))
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integral of 1/(sqrt(2-3x^2))
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\int\:\frac{1}{\sqrt{2-3x^{2}}}dx
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limit as x approaching-infinity of (5+4e^{2x})/(6-3e^{3x)}
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\lim_{x\to\:-\infty\:}(\frac{5+4e^{2x}}{6-3e^{3x}})
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limit as x approaching infinity of ((x^2-1))/((x^2-4))
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\lim_{x\to\:\infty\:}(\frac{(x^{2}-1)}{(x^{2}-4)})
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limit as x approaching+infinity+of (x^2-x-6)/(x^2+3x+2)
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\lim_{x\to\:+\infty\:+}(\frac{x^{2}-x-6}{x^{2}+3x+2})
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limit as x approaching π-of cot(x)
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\lim_{x\to\:π-}(\cot(x))
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limit as x approaching 0 of ((x^7))/(x^8-x^7)
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\lim_{x\to\:0}(\frac{(x^{7})}{x^{8}-x^{7}})
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limit as x approaching 0 of (1-cos(5x))/(1+5x-e^{5x)}
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\lim_{x\to\:0}(\frac{1-\cos(5x)}{1+5x-e^{5x}})
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derivative of 8e^{4x}
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derivative\:of\:8e^{4x}
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slope xy-5y^2=4
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slope\:xy-5y^{2}=4
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limit as x approaching 0 of (sin(6)x^2)/(1-cos(4x))
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\lim_{x\to\:0}(\frac{\sin(6)x^{2}}{1-\cos(4x)})
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partial derivative of-50e^{-(x-1^2-(y-1)^3}(x-1))
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\frac{\partial}{\partial\:x}(-50e^{-(x-1)^{2}-(y-1)^{3}}(x-1))
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limit as x approaching-infinity of (e^x)/x
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\lim_{x\to\:-\infty\:}(\frac{e^{x}}{x})
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limit as x approaching-infinity of (x^2-1)/(x^3+1)
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\lim_{x\to\:-\infty\:}(\frac{x^{2}-1}{x^{3}+1})
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laplace 4te^{3t}sin(2t)
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laplace\:4te^{3t}\sin(2t)
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integral from 3 to 7 of integral from 3 to 7 of e^{x+y}
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\int_{\:3}^{7}\int_{3}^{7}e^{x+y}dxdy
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(\partial)/(\partial x^2)(x^2y^2-y^3+3x^4+5)
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\frac{\partial}{\partial\:x^{2}}(x^{2}y^{2}-y^{3}+3x^{4}+5)
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integral of sqrt(18-18sin(x))
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\int\:\sqrt{18-18\sin(x)}dx
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limit as x approaching infinity of \sqrt[n]{infinity}
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\lim_{x\to\:\infty\:}(\sqrt[n]{\infty\:})
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limit as x approaching infinity of 1/(x!)
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\lim_{x\to\:\infty\:}(\frac{1}{x!})
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derivative of-1/(x^{2/3)}
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derivative\:of\:-\frac{1}{x^{\frac{2}{3}}}
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implicit derivative (dx)/(dy),ysec(x)=3xtan(y)
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implicit\:derivative\:\frac{dx}{dy},y\sec(x)=3x\tan(y)
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implicit derivative (dy)/(dx),xy^6-y=x
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implicit\:derivative\:\frac{dy}{dx},xy^{6}-y=x
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derivative of sinh^2(3x)
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\frac{d}{dx}(\sinh^{2}(3x))
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y^{\prime \prime}+4y=0,y(0)=4,y^{\prime}(0)=1
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y^{\prime\:\prime\:}+4y=0,y(0)=4,y^{\prime\:}(0)=1
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integral of (cos(9x))
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\int\:(\cos(9x))dx
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integral from 0 to (pi)/4 of tan^3(xse)c^2x
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\int_{\:0}^{\frac{\pi}{4}}\tan^{3}(xse)c^{2}xdx
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implicit derivative (dy)/(dx),x^3+3x^2y+y^3=8
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implicit\:derivative\:\frac{dy}{dx},x^{3}+3x^{2}y+y^{3}=8
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limit as x approaching 3 of (x-3)/(x^2+3x-18)
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\lim_{x\to\:3}(\frac{x-3}{x^{2}+3x-18})
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derivative of 2xe^x+3sec(x)
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\frac{d}{dx}(2xe^{x}+3\sec(x))
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derivative of ln((ax^n))
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\frac{d}{dx}(\ln((ax)^{n}))
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integral from-infinity to infinity of (19)/(x^2)
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\int_{\:-\infty\:}^{\infty\:}\frac{19}{x^{2}}dx
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(dy)/(dx)=y(1-y),y(0)=8
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\frac{dy}{dx}=y(1-y),y(0)=8
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integral of cos(x)sec^3(x)
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\int\:\cos(x)\sec^{3}(x)dx
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limit as x approaching 4-of 3x-5
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\lim_{x\to\:4-}(3x-5)
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derivative of 4x^3-56x^2+196x
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derivative\:of\:4x^{3}-56x^{2}+196x
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integral of 1/((sin(x)+cos(x))^2)
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\int\:\frac{1}{(\sin(x)+\cos(x))^{2}}dx
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integral of 2x^3e^{-2x}
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\int\:2x^{3}e^{-2x}dx
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limit as x approaching π/4 of (cos(2x))/(sqrt(2)cos(x)-1)
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\lim_{x\to\:\frac{π}{4}}(\frac{\cos(2x)}{\sqrt{2}\cos(x)-1})
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cos^2(x)sin(x)dy+(ycos^3(x)-1)dx=0
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\cos^{2}(x)\sin(x)dy+(y\cos^{3}(x)-1)dx=0
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x^2(dy)/(dx)+2xy=5y^3
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x^{2}\frac{dy}{dx}+2xy=5y^{3}
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limit as x approaching infinity of e^{-x}+6cos(8x)
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\lim_{x\to\:\infty\:}(e^{-x}+6\cos(8x))
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limit as x approaching-7 of (6x+42)/((x+7))
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\lim_{x\to\:-7}(\frac{6x+42}{(x+7)})
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derivative of 6ln(x^2)
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\frac{d}{dx}(6\ln(x^{2}))
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limit as x approaching 0 of \sqrt[3]{x}ln(x)
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\lim_{x\to\:0}(\sqrt[3]{x}\ln(x))
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integral of x*tan^2(x)
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\int\:x\cdot\:\tan^{2}(x)dx
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limit as x approaching 0 of sqrt(3x+1)
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\lim_{x\to\:0}(\sqrt{3x+1})
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derivative of 2sqrt(x)
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derivative\:of\:2\sqrt{x}
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(y^{\prime}-e^{-t}+3)/y =-3
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\frac{y^{\prime\:}-e^{-t}+3}{y}=-3
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integral of sqrt((1+sin(θ))^2+(cos(θ))^2)
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\int\:\sqrt{(1+\sin(θ))^{2}+(\cos(θ))^{2}}dθ
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limit as x approaching 0 of (sin(4x))/(tan(7x))
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\lim_{x\to\:0}(\frac{\sin(4x)}{\tan(7x)})
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limit as (x,y) approaching (0,0) of (9xy^2)/(x^2+y^2)
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\lim_{(\:x,y)\to\:(0,0)}(\frac{9xy^{2}}{x^{2}+y^{2}})
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limit as n approaching infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n)
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\lim_{n\to\:\infty\:}(\sum_{i=1}^{n}(1+\frac{2i}{n})^{3}(\frac{2}{n}))
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derivative of (x^3+x-2/(x-x^2))
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\frac{d}{dx}(\frac{x^{3}+x-2}{x-x^{2}})
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limit as x approaching 1 of (x^2-1)/(x^4-1)
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\lim_{x\to\:1}(\frac{x^{2}-1}{x^{4}-1})
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derivative of e^{(1-x^2-(y^2/4)})
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\frac{d}{dx}(e^{(1-x^{2}-\frac{y^{2}}{4})})
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derivative of e^{3e^x}
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derivative\:of\:e^{3e^{x}}
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tangent of f(x)=2x^2,\at x=-1
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tangent\:of\:f(x)=2x^{2},\at\:x=-1
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derivative of (-10/(\sqrt[3]{x)})
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\frac{d}{dx}(\frac{-10}{\sqrt[3]{x}})
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integral of (cos(x))/(3-cos^2(x)+4sin(x))
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\int\:\frac{\cos(x)}{3-\cos^{2}(x)+4\sin(x)}dx
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integral from 2 to 6 of (1/(sqrt(x-2)))
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\int_{\:2}^{6}(\frac{1}{\sqrt{x-2}})dx
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limit as x approaching 1 of ln|ln(x)|
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\lim_{x\to\:1}(\ln|\ln(x)|)
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partial derivative of ((x-1)/((x^2+2x+1)))
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\frac{\partial}{\partial\:x}(\frac{(x-1)}{(x^{2}+2x+1)})
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(dy)/(dt)=8y
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\frac{dy}{dt}=8y
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sum from n=0 to infinity of 1/(sqrt(n)+1)
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\sum_{n=0}^{\infty\:}\frac{1}{\sqrt{n}+1}
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derivative of f(x)=(x^3+3x+2)/(x^2-1)
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derivative\:of\:f(x)=\frac{x^{3}+3x+2}{x^{2}-1}
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(dy)/(dx)=x^3+2x+pi
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\frac{dy}{dx}=x^{3}+2x+\pi
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integral from-1 to 2 of (-x^2+x+2)
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\int_{\:-1}^{2}(-x^{2}+x+2)dx
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derivative of tan(x^3)
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\frac{d}{dx}(\tan(x^{3}))
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limit as t approaching infinity of 4e^{-t}
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\lim_{t\to\:\infty\:}(4e^{-t})
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derivative of (sin^2(x))/(cos^2(x))
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derivative\:of\:\frac{\sin^{2}(x)}{\cos^{2}(x)}
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limit as x approaching 64 of (x-8)/(\sqrt[3]{x)-4}
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\lim_{x\to\:64}(\frac{x-8}{\sqrt[3]{x}-4})
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limit as x approaching 4+of 2x-7
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\lim_{x\to\:4+}(2x-7)
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