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Popular Calculus Problems

limit as x approaches 0+of sin((5pi)/6 e^{sqrt(x)})	\lim\:_{x\to\:0+}(\sin(\frac{5π}{6}e^{\sqrt{x}}))
integral of (x+1)[ln(x+1)+c]	\int\:(x+1)[\ln(x+1)+c]dx
y^2y^'=y^2	y^{2}y^{\prime\:}=y^{2}
tangent of f(x)=x^2-2x	tangent\:f(x)=x^{2}-2x
integral of (x^3)/(sqrt(x^2+9))	\int\:\frac{x^{3}}{\sqrt{x^{2}+9}}dx
derivative of (-2x^2-2/((x-1)^2(x+1)^2))	\frac{d}{dx}(\frac{-2x^{2}-2}{(x-1)^{2}(x+1)^{2}})
area x=(y-1)^2,x=13-y^2	area\:x=(y-1)^{2},x=13-y^{2}
integral of (2x)/(e^{2x)}	\int\:\frac{2x}{e^{2x}}dx
limit as x approaches 2+of g(x)	\lim\:_{x\to\:2+}(g(x))
derivative of arctan(8^x)	\frac{d}{dx}(\arctan(8^{x}))
integral of-0.006t^2+0.2t	\int\:-0.006t^{2}+0.2tdt
(\partial)/(\partial x)(3x-y-1)	\frac{\partial\:}{\partial\:x}(3x-y-1)
integral of y/(x^2y^2+1)	\int\:\frac{y}{x^{2}y^{2}+1}dx
derivative of 9-x^2	derivative\:9-x^{2}
derivative of [x+(x+sin^2(x)^5]^4)	\frac{d}{dx}([x+(x+\sin^{2}(x))^{5}]^{4})
y^{''}-4y^'+20y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+20y=0
derivative of f(x)=(x-1)(x+1)^3	derivative\:f(x)=(x-1)(x+1)^{3}
derivative of 2sqrt(x)tanh(sqrt(x))	\frac{d}{dx}(2\sqrt{x}\tanh(\sqrt{x}))
derivative of-9/((6t+8)^{3/2)}	derivative\:-\frac{9}{(6t+8)^{\frac{3}{2}}}
limit as x approaches 1-of 4/(x^3-1)	\lim\:_{x\to\:1-}(\frac{4}{x^{3}-1})
derivative of 3(x^3+cos(x))	\frac{d}{dx}(3(x)^{3}+\cos(x))
limit as x approaches 0 of x^2csc^2(x)	\lim\:_{x\to\:0}(x^{2}\csc^{2}(x))
derivative of tan(x-x+1)	\frac{d}{dx}(\tan(x)-x+1)
derivative of sqrt(1+x^{256)}-1	\frac{d}{dx}(\sqrt{1+x^{256}}-1)
derivative of f(x)=19xe^x	derivative\:f(x)=19xe^{x}
integral of sin(x)e^{3x}	\int\:\sin(x)e^{3x}dx
integral of x^2cos(1/9 x)	\int\:x^{2}\cos(\frac{1}{9}x)dx
derivative of sec(xtan^2(x))	\frac{d}{dx}(\sec(x)\tan^{2}(x))
(\partial)/(\partial x)((x^2-y)/(x^2+y))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-y}{x^{2}+y})
integral of (8cosh(sqrt(x)))/(sqrt(x))	\int\:\frac{8\cosh(\sqrt{x})}{\sqrt{x}}dx
integral of ((5-x))/(2x^2+x-1)	\int\:\frac{(5-x)}{2x^{2}+x-1}dx
limit as z approaches 2 of (z^2+3)/(iz)	\lim\:_{z\to\:2}(\frac{z^{2}+3}{iz})
taylor ln(1+7x)	taylor\:\ln(1+7x)
(d^2)/(dx^2)(4x+15)	\frac{d^{2}}{dx^{2}}(4x+15)
(\partial)/(\partial x)(sqrt(xx+yy))	\frac{\partial\:}{\partial\:x}(\sqrt{xx+yy})
integral from 0 to pi of x*cos(x)	\int\:_{0}^{π}x\cdot\:\cos(x)dx
derivative of-xy^2	\frac{d}{dx}(-xy^{2})
tangent of f(x)=e^x+1,\at x=0	tangent\:f(x)=e^{x}+1,\at\:x=0
tangent of f(x)= 4/(x^5)-1/(x^2),\at x=1	tangent\:f(x)=\frac{4}{x^{5}}-\frac{1}{x^{2}},\at\:x=1
derivative of y=x^3-13x^2+48x+8	derivative\:y=x^{3}-13x^{2}+48x+8
(\partial)/(\partial x)(5y)	\frac{\partial\:}{\partial\:x}(5y)
(\partial)/(\partial x)(sqrt(6-x^7-y^5))	\frac{\partial\:}{\partial\:x}(\sqrt{6-x^{7}-y^{5}})
derivative of arctan(x+2)	\frac{d}{dx}(\arctan(x+2))
derivative of sin(x-y)	\frac{d}{dx}(\sin(x-y))
integral of (20x^3)/(3+5x^4)	\int\:\frac{20x^{3}}{3+5x^{4}}dx
(\partial)/(\partial x)(x^2-y^2+2xy)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{2}+2xy)
(\partial)/(\partial x)((2x+7y)^{11})	\frac{\partial\:}{\partial\:x}((2x+7y)^{11})
integral of cos^2((npix)/L)	\int\:\cos^{2}(\frac{nπx}{L})dx
integral of \sqrt[4]{x^3}+\sqrt[3]{x^4}	\int\:\sqrt[4]{x^{3}}+\sqrt[3]{x^{4}}dx
tangent of (x+2)^2+(y-3)^2=37,(-3,9)	tangent\:(x+2)^{2}+(y-3)^{2}=37,(-3,9)
derivative of y=sqrt(x^2+9)	derivative\:y=\sqrt{x^{2}+9}
(d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(1+x^2)	\frac{d^{2}y}{dx^{2}}-2\frac{dy}{dx}+y=\frac{e^{x}}{1+x^{2}}
limit as n approaches infinity of {(1+2/n)^{4n}}	\lim\:_{n\to\:\infty\:}(\left\{(1+\frac{2}{n})^{4n}\right\})
derivative of y=x^2e^x-2xe^x+9e^x	derivative\:y=x^{2}e^{x}-2xe^{x}+9e^{x}
(dy)/(dx)-2y=-1	\frac{dy}{dx}-2y=-1
y^'=0.2x	y^{\prime\:}=0.2x
integral from 1 to e^3 of x^5ln(x)	\int\:_{1}^{e^{3}}x^{5}\ln(x)dx
derivative of 8x^6	\frac{d}{dx}(8x^{6})
limit as x approaches infinity of e^{2x}	\lim\:_{x\to\:\infty\:}(e^{2x})
derivative of f(x)=(3x-9)/(x+5)	derivative\:f(x)=\frac{3x-9}{x+5}
sum from n=1 to infinity of (0.01)^n	\sum\:_{n=1}^{\infty\:}(0.01)^{n}
derivative of 5cos^2(x)	\frac{d}{dx}(5\cos^{2}(x))
tangent of f(x)=(2x-1)/(x+1),\at x=4	tangent\:f(x)=\frac{2x-1}{x+1},\at\:x=4
integral of (x+1/x)^{3/2}((x^2-1)/(x^2))	\int\:(x+\frac{1}{x})^{\frac{3}{2}}(\frac{x^{2}-1}{x^{2}})dx
(\partial)/(\partial y)(7x^2+e^{2y})	\frac{\partial\:}{\partial\:y}(7x^{2}+e^{2y})
integral of 4x(x^2+26000)^{-2/3}	\int\:4x(x^{2}+26000)^{-\frac{2}{3}}dx
tangent of f(x)=(x-4)(3-x)^3	tangent\:f(x)=(x-4)(3-x)^{3}
derivative of (x-2^2*(x+4))	\frac{d}{dx}((x-2)^{2}\cdot\:(x+4))
derivative of (2cos(x)/(x+1))	\frac{d}{dx}(\frac{2\cos(x)}{x+1})
limit as x approaches 0+of sqrt(x)	\lim\:_{x\to\:0+}(\sqrt{x})
y^'+y=e^xsin(e^x)	y^{\prime\:}+y=e^{x}\sin(e^{x})
y^'-(y-1)^2=0	y^{\prime\:}-(y-1)^{2}=0
integral of sqrt(X)	\int\:\sqrt{X}dX
limit as x approaches 0 of (1+1/x)^{5x}	\lim\:_{x\to\:0}((1+\frac{1}{x})^{5x})
integral from 6 to 8 of (14)/((x-6)^3)	\int\:_{6}^{8}\frac{14}{(x-6)^{3}}dx
limit as x approaches a of ((sin(x))/(sin(a)))^{1/(x+a)}	\lim\:_{x\to\:a}((\frac{\sin(x)}{\sin(a)})^{\frac{1}{x+a}})
integral of (2x+1)/(3x^2+3x+4)	\int\:\frac{2x+1}{3x^{2}+3x+4}dx
area 3x+3,4x+4,-1,3	area\:3x+3,4x+4,-1,3
(\partial)/(\partial x)(ln(2xy+4))	\frac{\partial\:}{\partial\:x}(\ln(2xy+4))
(\partial)/(\partial y)(arctan(x+6y))	\frac{\partial\:}{\partial\:y}(\arctan(x+6y))
derivative of y=sqrt(x^2+3)	derivative\:y=\sqrt{x^{2}+3}
integral from 1 to 4 of 7/(x^2)	\int\:_{1}^{4}\frac{7}{x^{2}}dx
(9x+3)+(9y-9)y^'=0	(9x+3)+(9y-9)y^{\prime\:}=0
integral from 0 to 3 of (x+sqrt(9-x^2))	\int\:_{0}^{3}(x+\sqrt{9-x^{2}})dx
integral from 1 to 2 of cos(x^2)	\int\:_{1}^{2}\cos(x^{2})dx
(\partial)/(\partial y)(x^2+xy)	\frac{\partial\:}{\partial\:y}(x^{2}+xy)
derivative of (9sqrt(x)/x)	\frac{d}{dx}(\frac{9\sqrt{x}}{x})
integral of (2-x)/(sqrt(x))	\int\:\frac{2-x}{\sqrt{x}}dx
derivative of cos^2(1-x^2)	\frac{d}{dx}(\cos^{2}(1-x^{2}))
derivative of (1-4t)/(3+t)	derivative\:\frac{1-4t}{3+t}
integral of ((2z-1))/(2z^2-6z+5)	\int\:\frac{(2z-1)}{2z^{2}-6z+5}dz
(9x+1)y^2(dy)/(dx)+4x^2+3y^3=0	(9x+1)y^{2}\frac{dy}{dx}+4x^{2}+3y^{3}=0
derivative of (x^{3.8}/(6^x))	\frac{d}{dx}(\frac{x^{3.8}}{6^{x}})
derivative of tan^2(6θ)	derivative\:\tan^{2}(6θ)
inverse oflaplace 1/(s^3(s-1))	inverselaplace\:\frac{1}{s^{3}(s-1)}
(\partial)/(\partial x)(cos(2y-2x))	\frac{\partial\:}{\partial\:x}(\cos(2y-2x))
integral of (3x^2-2x+1)(x^3-x^2+x)^4	\int\:(3x^{2}-2x+1)(x^{3}-x^{2}+x)^{4}dx
limit as x approaches 3 of x^2+7x-5	\lim\:_{x\to\:3}(x^{2}+7x-5)
derivative of x^2cos(y)	\frac{d}{dx}(x^{2}\cos(y))
derivative of (x^2+18(2x+15))	\frac{d}{dx}((x^{2}+18)(2x+15))

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