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Popular Calculus Problems

derivative of log_{ln(x}(e))	\frac{d}{dx}(\log_{\ln(x)}(e))
integral of 3/x	\int\:\frac{3}{x}dx
limit as x approaches 0 of (x^3-1)/(x-1)	\lim\:_{x\to\:0}(\frac{x^{3}-1}{x-1})
area x=y^2,x=36-y^2	area\:x=y^{2},x=36-y^{2}
derivative of y= x/8-8/x	derivative\:y=\frac{x}{8}-\frac{8}{x}
integral from t to 1 of 1/(sqrt(x-1))	\int\:_{t}^{1}\frac{1}{\sqrt{x-1}}dx
derivative of (x-2/(x+3))	\frac{d}{dx}(\frac{x-2}{x+3})
(\partial)/(\partial x)(2xcos(x+2y))	\frac{\partial\:}{\partial\:x}(2x\cos(x+2y))
integral of x^5sin(x)	\int\:x^{5}\sin(x)dx
integral of cos(x)cos^3(sin(x))	\int\:\cos(x)\cos^{3}(\sin(x))dx
derivative of f(x)=3xln(5x)-3x	derivative\:f(x)=3x\ln(5x)-3x
(1+x^2)y^'-2xy=x^2+x^4	(1+x^{2})y^{\prime\:}-2xy=x^{2}+x^{4}
area y=x^4+x^3,y=x^4+x^2+6x	area\:y=x^{4}+x^{3},y=x^{4}+x^{2}+6x
derivative of Ae^{4x}	\frac{d}{dx}(Ae^{4x})
(\partial)/(\partial v)(2u+v)	\frac{\partial\:}{\partial\:v}(2u+v)
derivative of sqrt(ln(7x+9))	derivative\:\sqrt{\ln(7x+9)}
integral of x^23^x	\int\:x^{2}3^{x}dx
integral of x^2+x+3	\int\:x^{2}+x+3dx
limit as x approaches 0+of (x^2)/6-7/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{6}-\frac{7}{x})
derivative of (3(9^x)/(x^5))	\frac{d}{dx}(\frac{3(9^{x})}{x^{5}})
integral of 1/(x^5)sin(1/(x^4))	\int\:\frac{1}{x^{5}}\sin(\frac{1}{x^{4}})dx
y^'-4y^2=2ty^2	y^{\prime\:}-4y^{2}=2ty^{2}
2x^3y^'=y(2x^2-y^2)	2x^{3}y^{\prime\:}=y(2x^{2}-y^{2})
tangent of f(x)=12(x-1/x)^2,\at x=2	tangent\:f(x)=12(x-\frac{1}{x})^{2},\at\:x=2
integral of ((e^x+e^{-x}))/2	\int\:\frac{(e^{x}+e^{-x})}{2}dx
limit as x approaches 0 of (2x)/x	\lim\:_{x\to\:0}(\frac{2x}{x})
limit as x approaches-4-of 2/(x^2-16)	\lim\:_{x\to\:-4-}(\frac{2}{x^{2}-16})
(dy)/(dx)=((e^x-e^{-x}))/(3+y)	\frac{dy}{dx}=\frac{(e^{x}-e^{-x})}{3+y}
integral of (2x)/((x+1)^2)	\int\:\frac{2x}{(x+1)^{2}}dx
derivative of 5e^xcos(x)	derivative\:5e^{x}\cos(x)
derivative of h(x)=ln(x+sqrt(x^2-6))	derivative\:h(x)=\ln(x+\sqrt{x^{2}-6})
integral of e^x4x	\int\:e^{x}4xdx
integral from-1 to 1 of e^xcos(npix)	\int\:_{-1}^{1}e^{x}\cos(nπx)dx
limit as x approaches-3 of (x+3)/(x^2-9)	\lim\:_{x\to\:-3}(\frac{x+3}{x^{2}-9})
derivative of f(x)=2xe^x	derivative\:f(x)=2xe^{x}
integral of ((x+5)/(x^2+x-6))	\int\:(\frac{x+5}{x^{2}+x-6})dx
integral of (4x)/(sqrt(x^2-1))	\int\:\frac{4x}{\sqrt{x^{2}-1}}dx
derivative of f(x)=arctan(x/2)	derivative\:f(x)=\arctan(\frac{x}{2})
(sin(1/x))^'	(\sin(\frac{1}{x}))^{\prime\:}
xy^'+y=-8xy^2,y(1)=3	xy^{\prime\:}+y=-8xy^{2},y(1)=3
inverse oflaplace (s+1)/(s^2+4s+8)	inverselaplace\:\frac{s+1}{s^{2}+4s+8}
integral of xsin(3x^2+10)	\int\:x\sin(3x^{2}+10)dx
d/(d{x)}(ln({x}{y}{z}))	\frac{d}{d{x}}(\ln({x}{y}{z}))
integral of 1/(xsqrt(a^2+x^2))	\int\:\frac{1}{x\sqrt{a^{2}+x^{2}}}dx
sum from n=3 to infinity of 2/(n^2-1)	\sum\:_{n=3}^{\infty\:}\frac{2}{n^{2}-1}
(\partial)/(\partial y)(2x+y+1)	\frac{\partial\:}{\partial\:y}(2x+y+1)
derivative of (x^2)/(6+sqrt(x))	derivative\:\frac{x^{2}}{6+\sqrt{x}}
limit as x approaches-1 of-x^2+4x-5	\lim\:_{x\to\:-1}(-x^{2}+4x-5)
derivative of (2x^2/((x^2+x)^3))	\frac{d}{dx}(\frac{2x^{2}}{(x^{2}+x)^{3}})
tangent of f(x)=4x^2-2x+4,\at x=0	tangent\:f(x)=4x^{2}-2x+4,\at\:x=0
tangent of f(x)=-2x^4+5x^2-3,(1,0)	tangent\:f(x)=-2x^{4}+5x^{2}-3,(1,0)
(d^2)/(dx^2)(1/(sqrt(x)))	\frac{d^{2}}{dx^{2}}(\frac{1}{\sqrt{x}})
(\partial)/(\partial x)(y/(2x+y))	\frac{\partial\:}{\partial\:x}(\frac{y}{2x+y})
integral of (sin(sqrt(t)))/(sqrt(t))	\int\:\frac{\sin(\sqrt{t})}{\sqrt{t}}dt
(y-x4)dx+(x+y4)dy=0	(y-x4)dx+(x+y4)dy=0
(dy)/(dx)=4xe^{2x}	\frac{dy}{dx}=4xe^{2x}
(\partial)/(\partial x)(sqrt(x)+ln(5x+y))	\frac{\partial\:}{\partial\:x}(\sqrt{x}+\ln(5x+y))
(\partial)/(\partial y)(cos(2x)y)	\frac{\partial\:}{\partial\:y}(\cos(2x)y)
integral of 1/(y^4sqrt(y^2-5))	\int\:\frac{1}{y^{4}\sqrt{y^{2}-5}}dy
derivative of ln(kx)	derivative\:\ln(kx)
integral of x/(sqrt(1+6x-3x^2))	\int\:\frac{x}{\sqrt{1+6x-3x^{2}}}dx
(\partial)/(\partial y)(x^2-x)	\frac{\partial\:}{\partial\:y}(x^{2}-x)
derivative of pi/2 x	\frac{d}{dx}(\frac{π}{2}x)
integral from 0 to 2 of (xsqrt(x^2+5))	\int\:_{0}^{2}(x\sqrt{x^{2}+5})dx
integral of (1+e^{2x})^2	\int\:(1+e^{2x})^{2}dx
inverse oflaplace 1/((s^2+1)(s+1))	inverselaplace\:\frac{1}{(s^{2}+1)(s+1)}
integral from 0 to 4 of xsqrt(23-x^2)	\int\:_{0}^{4}x\sqrt{23-x^{2}}dx
integral of e^{-2sqrt(x)}	\int\:e^{-2\sqrt{x}}dx
integral of (e^{-2x})/x	\int\:\frac{e^{-2x}}{x}dx
(\partial)/(\partial x)((x-1)^2+(y-1)^2)	\frac{\partial\:}{\partial\:x}((x-1)^{2}+(y-1)^{2})
integral from-infinity to 0 of 1/(2-8x)	\int\:_{-\infty\:}^{0}\frac{1}{2-8x}dx
integral of (8x^2)/(sqrt(25-x^2))	\int\:\frac{8x^{2}}{\sqrt{25-x^{2}}}dx
integral of (2x-4)^5	\int\:(2x-4)^{5}dx
derivative of e^{tan(3x})	\frac{d}{dx}(e^{\tan(3x)})
d/(dt)(t/2)	\frac{d}{dt}(\frac{t}{2})
integral from 0 to pi/2 of sin^7(y)	\int\:_{0}^{\frac{π}{2}}\sin^{7}(y)dy
integral of 1-(-2sin^2(x+4))^2	\int\:1-(-2\sin^{2}(x+4))^{2}dx
inverse oflaplace 3/s	inverselaplace\:\frac{3}{s}
(d^2)/(dx^2)((x^2+6x)/(x^2-9))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}+6x}{x^{2}-9})
integral of sqrt(4096-x^2)	\int\:\sqrt{4096-x^{2}}dx
integral of (cos(3pix))/2	\int\:\frac{\cos(3πx)}{2}dx
d/(dn)(1/n)	\frac{d}{dn}(\frac{1}{n})
integral of 4x^2-2x-2	\int\:4x^{2}-2x-2dx
derivative of 6xe^{5x}	derivative\:6xe^{5x}
limit as x approaches 1+of 6/(x^3-1)	\lim\:_{x\to\:1+}(\frac{6}{x^{3}-1})
integral from 0 to 1 of x^3e^{x^2}	\int\:_{0}^{1}x^{3}e^{x^{2}}dx
integral of (y^2)/(y^3+1)	\int\:\frac{y^{2}}{y^{3}+1}dy
derivative of sqrt(3x^2-x+1)	derivative\:\sqrt{3x^{2}-x+1}
slope of f(x)=x^2+6(-5.31)	slope\:f(x)=x^{2}+6(-5.31)
integral of 1/(1sqrt(x))	\int\:\frac{1}{1\sqrt{x}}dx
tangent of f(x)=x^3-6x,\at x=2	tangent\:f(x)=x^{3}-6x,\at\:x=2
f(x)=cos^3(2+x)	f(x)=\cos^{3}(2+x)
limit as h approaches 0 of (x+h)3-x^3h	\lim\:_{h\to\:0}((x+h)3-x^{3}h)
integral of (1+y^3)^2	\int\:(1+y^{3})^{2}dy
derivative of y=(3+xf(x))/(sqrt(x))	derivative\:y=\frac{3+xf(x)}{\sqrt{x}}
limit as x approaches-infinity of-1	\lim\:_{x\to\:-\infty\:}(-1)
integral from-3 to 4 of \|x\|	\int\:_{-3}^{4}\left\|x\right\|dx
derivative of x(x^5+5^3)	\frac{d}{dx}(x(x^{5}+5)^{3})
integral from 0 to 6 of 1/(sqrt(36+t^2))	\int\:_{0}^{6}\frac{1}{\sqrt{36+t^{2}}}dt
integral of (x+2)/x	\int\:\frac{x+2}{x}dx

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