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Popular Calculus Problems

integral of ((x-3)^3)/(x^2-9)	\int\:\frac{(x-3)^{3}}{x^{2}-9}dx
integral of (xsin(x))/(cos^2(x))	\int\:\frac{x\sin(x)}{\cos^{2}(x)}dx
(\partial)/(\partial x)(xyzln(x+y))	\frac{\partial\:}{\partial\:x}(xyz\ln(x+y))
limit as x approaches 4-of 8-2x	\lim\:_{x\to\:4-}(8-2x)
limit as x approaches-8-of (-2x)/(x+8)	\lim\:_{x\to\:-8-}(\frac{-2x}{x+8})
integral of pi(x+2)^2	\int\:π(x+2)^{2}dx
tangent of f(x)=sqrt(x+63),(1,8)	tangent\:f(x)=\sqrt{x+63},(1,8)
integral from 0 to 1 of tsqrt(1+4t^2)	\int\:_{0}^{1}t\sqrt{1+4t^{2}}dt
xy^'=y+e^{y/x}	xy^{\prime\:}=y+e^{\frac{y}{x}}
limit as x approaches 2 of-2	\lim\:_{x\to\:2}(-2)
(dx)/(dt)=xsin(t),x(0)=1	\frac{dx}{dt}=x\sin(t),x(0)=1
integral of 6tan(x)sec^3(x)	\int\:6\tan(x)\sec^{3}(x)dx
f(x)=8cos(x)	f(x)=8\cos(x)
integral of e^{-x^8}	\int\:e^{-x^{8}}dx
area y=x^2-2x,y=x	area\:y=x^{2}-2x,y=x
xy'+2y=x+2	xy\prime\:+2y=x+2
integral of (\sqrt[5]{4x^2+5})/3 x	\int\:\frac{\sqrt[5]{4x^{2}+5}}{3}xdx
derivative of 3sqrt(x)-6\sqrt[3]{x}	\frac{d}{dx}(3\sqrt{x}-6\sqrt[3]{x})
sum from n=1 to infinity of n^{(-2/3)}	\sum\:_{n=1}^{\infty\:}n^{(-\frac{2}{3})}
derivative of (x+2^{-1})	\frac{d}{dx}((x+2)^{-1})
derivative of sqrt(x-2)	derivative\:\sqrt{x-2}
limit as x approaches-5 of x^2	\lim\:_{x\to\:-5}(x^{2})
sum from n=1.0E22 to infinity of 1/n	\sum\:_{n=1.0E22}^{\infty\:}\frac{1}{n}
integral from 0 to 1 of (3x+1)^{sqrt(2)}	\int\:_{0}^{1}(3x+1)^{\sqrt{2}}dx
derivative of f(x)=sqrt(8x+1)	derivative\:f(x)=\sqrt{8x+1}
inverse oflaplace (7s+10)/(7s^2+26s+25)	inverselaplace\:\frac{7s+10}{7s^{2}+26s+25}
f(x)=-tan(x)	f(x)=-\tan(x)
derivative of y=e^{4x^2}	derivative\:y=e^{4x^{2}}
integral from-2 to 3 of (30)/(x^4)	\int\:_{-2}^{3}\frac{30}{x^{4}}dx
integral of-y/(z^2)	\int\:-\frac{y}{z^{2}}dz
integral of 1/(sqrt(-x^2-18x))	\int\:\frac{1}{\sqrt{-x^{2}-18x}}dx
integral of (10)/((t^2+1)^{3/2)}	\int\:\frac{10}{(t^{2}+1)^{\frac{3}{2}}}dt
integral of 1/((x-5)^2)	\int\:\frac{1}{(x-5)^{2}}dx
limit as x approaches 3 of (x-5)/(\|x-5\|)	\lim\:_{x\to\:3}(\frac{x-5}{\left\|x-5\right\|})
(sinh(x))^'	(\sinh(x))^{\prime\:}
sum from n=1 to infinity of e^{-n}	\sum\:_{n=1}^{\infty\:}e^{-n}
integral of 6sin(3x)ln(sin(3x))	\int\:6\sin(3x)\ln(\sin(3x))dx
derivative of (\sqrt[4]{x}^{ln(x)})	\frac{d}{dx}((\sqrt[4]{x})^{\ln(x)})
(dx)/(dt)=2x+t+1	\frac{dx}{dt}=2x+t+1
25y^{''}-30y^'+9y=0	25y^{\prime\:\prime\:}-30y^{\prime\:}+9y=0
integral of 1/(2t^2+3t+1)	\int\:\frac{1}{2t^{2}+3t+1}dt
derivative of y= x/(2x-4)	derivative\:y=\frac{x}{2x-4}
derivative of ({r}(x)/x)	\frac{d}{dx}(\frac{{r}(x)}{x})
f(x)=e^{sqrt(x)}	f(x)=e^{\sqrt{x}}
tangent of y=6x^2+3x-9	tangent\:y=6x^{2}+3x-9
integral of e^{-2u}	\int\:e^{-2u}du
integral from 1 to 3 of (3x+2)^2	\int\:_{1}^{3}(3x+2)^{2}dx
integral from 0 to x^2 of xsin(t^2)	\int\:_{0}^{x^{2}}x\sin(t^{2})dt
(\partial)/(\partial x)(x/(3+6x^2+7y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{3+6x^{2}+7y^{2}})
derivative of 1/(x-1+1/(4-x))	\frac{d}{dx}(\frac{1}{x-1}+\frac{1}{4-x})
derivative of arcsin(xy)	\frac{d}{dx}(\arcsin(xy))
f(x)=(xe^x)/(x+e^x)	f(x)=\frac{xe^{x}}{x+e^{x}}
integral of 4/((x+2)(x-2))	\int\:\frac{4}{(x+2)(x-2)}dx
y^'=(2cos(2x))/(3+2y),y(0)=-1	y^{\prime\:}=\frac{2\cos(2x)}{3+2y},y(0)=-1
integral from 0 to 1 of (x-1)/(x^2+3x+2)	\int\:_{0}^{1}\frac{x-1}{x^{2}+3x+2}dx
(\partial)/(\partial x)(ln(x+7y+8z))	\frac{\partial\:}{\partial\:x}(\ln(x+7y+8z))
integral of e^{2x}-e^{-x}	\int\:e^{2x}-e^{-x}dx
tangent of f(x)=(e^x)/x ,\at x=1	tangent\:f(x)=\frac{e^{x}}{x},\at\:x=1
(\partial)/(\partial x)(x^2y+y^2z+xz^2)	\frac{\partial\:}{\partial\:x}(x^{2}y+y^{2}z+xz^{2})
derivative of sqrt((3x+2/(5-4x)))	\frac{d}{dx}(\sqrt{\frac{3x+2}{5-4x}})
integral of x^7	\int\:x^{7}dx
integral of 2/(12-5x)	\int\:\frac{2}{12-5x}dx
derivative of arccos(x)	derivative\:\arccos(x)
maclaurin (1+x)^{-4/3}	maclaurin\:(1+x)^{-\frac{4}{3}}
(\partial)/(\partial x)(1/(ln(y/x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\ln(\frac{y}{x})})
inverse oflaplace (s^2)/((s^2+1)^2)	inverselaplace\:\frac{s^{2}}{(s^{2}+1)^{2}}
simplify ln(((x+6)^4e^{5x^3-3})/(x+2x^3))	simplify\:\ln(\frac{(x+6)^{4}e^{5x^{3}-3}}{x+2x^{3}})
tangent of y=x^2+4x+7,\at x=1	tangent\:y=x^{2}+4x+7,\at\:x=1
tangent of 7/(2sqrt(7x+1)),\at x=9	tangent\:\frac{7}{2\sqrt{7x+1}},\at\:x=9
derivative of ln(y^2)	derivative\:\ln(y^{2})
derivative of arctan(1-x)	\frac{d}{dx}(\arctan(1-x))
integral from 2 to 3 of 2x	\int\:_{2}^{3}2xdx
simplify 7/4 x^4-6/5 x^3	simplify\:\frac{7}{4}x^{4}-\frac{6}{5}x^{3}
limit as x approaches 0 of (e^x-1)/(17x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{17x})
derivative of f(x)=3^x-5e^x	derivative\:f(x)=3^{x}-5e^{x}
derivative of x^3-7	\frac{d}{dx}(x^{3}-7)
derivative of 1/(1+x)	derivative\:\frac{1}{1+x}
integral of 9xe^{(-3x)}	\int\:9xe^{(-3x)}dx
tangent of f(x)=3-x^2,\at x=4	tangent\:f(x)=3-x^{2},\at\:x=4
y^'=5-2y	y^{\prime\:}=5-2y
y^'=cos^2(y)	y^{\prime\:}=\cos^{2}(y)
tangent of y=(x^2)/(x+1),(2, 4/3)	tangent\:y=\frac{x^{2}}{x+1},(2,\frac{4}{3})
(dy)/(dx)+6xy^5=0	\frac{dy}{dx}+6xy^{5}=0
(7x+11y)dx+(11x+5y)dy=0,y(0)=2	(7x+11y)dx+(11x+5y)dy=0,y(0)=2
(\partial)/(\partial x)(y/(2sqrt(x))-4)	\frac{\partial\:}{\partial\:x}(\frac{y}{2\sqrt{x}}-4)
derivative of 2x^3-3x+1	\frac{d}{dx}(2x^{3}-3x+1)
laplacetransform 7cos(2t)	laplacetransform\:7\cos(2t)
integral of d	\int\:ddd
integral of (x+3)(x-2)	\int\:(x+3)(x-2)dx
derivative of 1/(sqrt(x^4))	\frac{d}{dx}(\frac{1}{\sqrt{x^{4}}})
inverse oflaplace 1/(4s^2+1)	inverselaplace\:\frac{1}{4s^{2}+1}
integral of cos(1/2)x	\int\:\cos(\frac{1}{2})xdx
ty^'+2y=sin(t),y(pi/2)=5	ty^{\prime\:}+2y=\sin(t),y(\frac{π}{2})=5
(\partial)/(\partial x)(6x-4y)	\frac{\partial\:}{\partial\:x}(6x-4y)
integral of sqrt((8+x^2))	\int\:\sqrt{(8+x^{2})}dx
integral of 1/(sqrt(8-2x^2))	\int\:\frac{1}{\sqrt{8-2x^{2}}}dx
integral of (2x)/(x^2+6x+5)	\int\:\frac{2x}{x^{2}+6x+5}dx
laplacetransform 3tcos(3t)	laplacetransform\:3t\cos(3t)
limit as x approaches 1 of e^{x-2}	\lim\:_{x\to\:1}(e^{x-2})
(\partial)/(\partial x)(2x^2y)	\frac{\partial\:}{\partial\:x}(2x^{2}y)

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