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Popular Calculus Problems

derivative of (125+x)^{-1/3}	derivative\:(125+x)^{-\frac{1}{3}}
integral of cos^3(3x)	\int\:\cos^{3}(3x)dx
y^'= y/((x^2+1)x)	y^{\prime\:}=\frac{y}{(x^{2}+1)x}
derivative of (20x/(x^2+2))	\frac{d}{dx}(\frac{20x}{x^{2}+2})
limit as x approaches 3 of 2/(x-2)	\lim\:_{x\to\:3}(\frac{2}{x-2})
inverse oflaplace ((e^{-2s}-2))/s	inverselaplace\:\frac{(e^{-2s}-2)}{s}
integral of xotx^2	\int\:xotx^{2}dx
(\partial)/(\partial x)(1+e^x)	\frac{\partial\:}{\partial\:x}(1+e^{x})
derivative of 1/(x*ln(x^9))	\frac{d}{dx}(\frac{1}{x\cdot\:\ln(x^{9})})
derivative of 2/(3x^3)	\frac{d}{dx}(\frac{2}{3x^{3}})
integral of 18x^{17}	\int\:18x^{17}dx
derivative of sqrt(x+\sqrt{x+\sqrt{x)}}	derivative\:\sqrt{x+\sqrt{x+\sqrt{x}}}
inverse oflaplace s/((s^2-1^2)(s^2+17))	inverselaplace\:\frac{s}{(s^{2}-1^{2})(s^{2}+17)}
limit as x approaches-infinity of e^x*x	\lim\:_{x\to\:-\infty\:}(e^{x}\cdot\:x)
integral of (x+10)/(x^2+6x+13)	\int\:\frac{x+10}{x^{2}+6x+13}dx
(\partial)/(\partial x)(-x+y)	\frac{\partial\:}{\partial\:x}(-x+y)
integral of x^2tan^3(x^3)	\int\:x^{2}\tan^{3}(x^{3})dx
(x^2+4)y^'+3xy=x,y(0)=1	(x^{2}+4)y^{\prime\:}+3xy=x,y(0)=1
area 9x^4-9x^2,8x^2	area\:9x^{4}-9x^{2},8x^{2}
integral from 0 to 1/10 of 1/((100x^2+1)^{3/2)}	\int\:_{0}^{\frac{1}{10}}\frac{1}{(100x^{2}+1)^{\frac{3}{2}}}dx
integral of ((sin(x)))/(cos^2(x))	\int\:\frac{(\sin(x))}{\cos^{2}(x)}dx
inverse oflaplace (s+5)/((s+2)(s+3))	inverselaplace\:\frac{s+5}{(s+2)(s+3)}
limit as x approaches infinity of 8/x-8	\lim\:_{x\to\:\infty\:}(\frac{8}{x}-8)
derivative of y=(cos(x))/(2+sin(x))	derivative\:y=\frac{\cos(x)}{2+\sin(x)}
derivative of cos(2x+pi)	derivative\:\cos(2x+π)
5ty^'+(10+5t((2(t-7))/(7t)))y=0	5ty^{\prime\:}+(10+5t(\frac{2(t-7)}{7t}))y=0
(\partial)/(\partial x)(10sin(xy))	\frac{\partial\:}{\partial\:x}(10\sin(xy))
integral of (12sqrt(x)+sqrt(7))	\int\:(12\sqrt{x}+\sqrt{7})dx
limit as x approaches 4 of 1/(x-3)	\lim\:_{x\to\:4}(\frac{1}{x-3})
derivative of-(170t)/((t+4)^2)	derivative\:-\frac{170t}{(t+4)^{2}}
limit as x approaches 1+of 3/(1-x)	\lim\:_{x\to\:1+}(\frac{3}{1-x})
(dy)/(dx)=3x+xy	\frac{dy}{dx}=3x+xy
9y^{''}+12y^'+4y=0	9y^{\prime\:\prime\:}+12y^{\prime\:}+4y=0
integral from 0 to 1 of (3x+1)^4	\int\:_{0}^{1}(3x+1)^{4}dx
tangent of f(x)= 1/(1+x^2),\at x=2	tangent\:f(x)=\frac{1}{1+x^{2}},\at\:x=2
(dx)/(dt)=x^2+1/49 ,x(0)=1	\frac{dx}{dt}=x^{2}+\frac{1}{49},x(0)=1
(x^2+1)y^'+6x(y-1)=0,y(0)=6	(x^{2}+1)y^{\prime\:}+6x(y-1)=0,y(0)=6
derivative of ln(x+1)	derivative\:\ln(x+1)
(d^3)/(dx^3)(sin(7x))	\frac{d^{3}}{dx^{3}}(\sin(7x))
y^{''}+6y^'+9y=0,y(1)=0,y^'(1)=1	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=0,y(1)=0,y^{\prime\:}(1)=1
tangent of f(x)=3-x-x^2,\at x=1	tangent\:f(x)=3-x-x^{2},\at\:x=1
derivative of sqrt(x^3)+4x^2-6x+1	\frac{d}{dx}(\sqrt{x^{3}}+4x^{2}-6x+1)
20y^{''}-11y^'-3y=0	20y^{\prime\:\prime\:}-11y^{\prime\:}-3y=0
integral of 5sin^3(5xco)s^35x	\int\:5\sin^{3}(5xco)s^{3}5xdx
integral from 9 to 10 of 1/((x-9)^{5/4)}	\int\:_{9}^{10}\frac{1}{(x-9)^{\frac{5}{4}}}dx
derivative of x/2-tan(x)	\frac{d}{dx}(\frac{x}{2}-\tan(x))
integral of sec(x)tan^3(x)	\int\:\sec(x)\tan^{3}(x)dx
limit as x approaches 3 of-x+2	\lim\:_{x\to\:3}(-x+2)
integral of (x^5)/((x^2+4)^2)	\int\:\frac{x^{5}}{(x^{2}+4)^{2}}dx
derivative of 6x^3-4x^2+5x	\frac{d}{dx}(6x^{3}-4x^{2}+5x)
tangent of f(x)=(9x)/(x+4),\at x=8	tangent\:f(x)=\frac{9x}{x+4},\at\:x=8
integral of-1/4 sin(2x)	\int\:-\frac{1}{4}\sin(2x)dx
derivative of f(x)=(6x)/(x+6)	derivative\:f(x)=\frac{6x}{x+6}
derivative of ln(3x^2+5)	\frac{d}{dx}(\ln(3x^{2}+5))
limit as x approaches 0+of x^2-ln(x)	\lim\:_{x\to\:0+}(x^{2}-\ln(x))
derivative of sqrt((x-4^3))	\frac{d}{dx}(\sqrt{(x-4)^{3}})
derivative of f(x)=(log_{9}(x))/(7+x^9)	derivative\:f(x)=\frac{\log_{9}(x)}{7+x^{9}}
derivative of g(x)=9e^xsqrt(x)	derivative\:g(x)=9e^{x}\sqrt{x}
derivative of (x^2/(1+2tan(x)))	\frac{d}{dx}(\frac{x^{2}}{1+2\tan(x)})
(\partial)/(\partial x)((x-y)/(3xy+2))	\frac{\partial\:}{\partial\:x}(\frac{x-y}{3xy+2})
integral of (2+ln(x))/(xln(x))	\int\:\frac{2+\ln(x)}{x\ln(x)}dx
tangent of y=3x^2+3x	tangent\:y=3x^{2}+3x
integral from 2 to infinity of 9/(x^2)	\int\:_{2}^{\infty\:}\frac{9}{x^{2}}dx
integral of 5xln(x^3)	\int\:5x\ln(x^{3})dx
area e^x,e^{-2x},x=ln(5)	area\:e^{x},e^{-2x},x=\ln(5)
integral of 28x^3-15x^2+8x	\int\:28x^{3}-15x^{2}+8xdx
derivative of (x-7)/(-5x-10)	derivative\:\frac{x-7}{-5x-10}
derivative of x^nln(x)	\frac{d}{dx}(x^{n}\ln(x))
inverse oflaplace 9/((s+3)^2)	inverselaplace\:\frac{9}{(s+3)^{2}}
derivative of-4/5 e^{(2/3 x})	\frac{d}{dx}(-\frac{4}{5}e^{(\frac{2}{3}x)})
integral of (2x+7)/((2x^2+14x)^4)	\int\:\frac{2x+7}{(2x^{2}+14x)^{4}}dx
integral of sin(x)(1+cos(x))^4	\int\:\sin(x)(1+\cos(x))^{4}dx
(\partial)/(\partial y)(x^2+y^2-z^2)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-z^{2})
laplacetransform e^{-t}((e^t+e^{-t})/2)	laplacetransform\:e^{-t}(\frac{e^{t}+e^{-t}}{2})
tangent of f(x)=(25x^3)/3+10x^2+4x-7	tangent\:f(x)=\frac{25x^{3}}{3}+10x^{2}+4x-7
limit as n approaches infinity of 4n	\lim\:_{n\to\:\infty\:}(4n)
(\partial)/(\partial x)(2x^{1/2}y^{1/3})	\frac{\partial\:}{\partial\:x}(2x^{\frac{1}{2}}y^{\frac{1}{3}})
y^'= y/2	y^{\prime\:}=\frac{y}{2}
derivative of-1/(ln(10x^2))	\frac{d}{dx}(-\frac{1}{\ln(10)x^{2}})
(x-2)e^{(-2y)}=(dy)/(dx)	(x-2)e^{(-2y)}=\frac{dy}{dx}
derivative of f(x)=sin(arcsin(6x))	derivative\:f(x)=\sin(\arcsin(6x))
integral of 1/(\frac{16x^2){3}-25}	\int\:\frac{1}{\frac{16x^{2}}{3}-25}dx
f(x)=-3sin(x)	f(x)=-3\sin(x)
integral of 1/2 (e^x-1)	\int\:\frac{1}{2}(e^{x}-1)dx
limit as x approaches 0 of (\|x\|)/x	\lim\:_{x\to\:0}(\frac{\left\|x\right\|}{x})
limit as x approaches 2 of sqrt(x+2)	\lim\:_{x\to\:2}(\sqrt{x+2})
derivative of f(x)= 1/(x-4)	derivative\:f(x)=\frac{1}{x-4}
(d^3)/(dx^3)(2/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{2}{x^{2}})
(\partial)/(\partial x)(2xe^{-y})	\frac{\partial\:}{\partial\:x}(2xe^{-y})
y^'+6y=60,y(1)=60	y^{\prime\:}+6y=60,y(1)=60
integral of 1/(1-tan^2(x))	\int\:\frac{1}{1-\tan^{2}(x)}dx
(dy)/(dx)=(x+y+2)/(x+y-4)	\frac{dy}{dx}=\frac{x+y+2}{x+y-4}
limit as x approaches 0 of x^2+2	\lim\:_{x\to\:0}(x^{2}+2)
derivative of cos(2x2)	\frac{d}{dx}(\cos(2x)2)
integral from-3 to-2 of 2x(4-x^2)^3	\int\:_{-3}^{-2}2x(4-x^{2})^{3}dx
(d^2)/(dx^2)(1/(1+x^2))	\frac{d^{2}}{dx^{2}}(\frac{1}{1+x^{2}})
integral of 1/((3-x)sqrt(2-x))	\int\:\frac{1}{(3-x)\sqrt{2-x}}dx
(\partial)/(\partial y)(x^2+xy+y^2+y)	\frac{\partial\:}{\partial\:y}(x^{2}+xy+y^{2}+y)
derivative of f(x)=(3x^3+1)^2	derivative\:f(x)=(3x^{3}+1)^{2}
limit as x approaches-8-of x^2+2/(x+8)	\lim\:_{x\to\:-8-}(x^{2}+\frac{2}{x+8})

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