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Popular Calculus Problems

derivative of (4x^5+7)/(x^3)	derivative\:\frac{4x^{5}+7}{x^{3}}
derivative of ln((x^2+1/(x+4)))	\frac{d}{dx}(\ln(\frac{x^{2}+1}{x+4}))
y^{''}+3y^'+2y=0,y(0)=2,y(1)=3	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=0,y(0)=2,y(1)=3
limit as x approaches 7+of ln(x-7)	\lim\:_{x\to\:7+}(\ln(x-7))
integral of e^{7x+9}	\int\:e^{7x+9}dx
integral of (sin(x))/(sqrt(2-cos^2(x)))	\int\:\frac{\sin(x)}{\sqrt{2-\cos^{2}(x)}}dx
derivative of e^{4x}cos(7x)	derivative\:e^{4x}\cos(7x)
tangent of f(x)=xsqrt(x),(4,8)	tangent\:f(x)=x\sqrt{x},(4,8)
limit as x approaches 0 of 10^{2x}	\lim\:_{x\to\:0}(10^{2x})
derivative of 120x	\frac{d}{dx}(120x)
integral of (x+2)sin^2(2θ)	\int\:(x+2)\sin^{2}(2θ)
limit as x approaches 0 of (4x^2-3x)/(x^2+0.8x+4/x)	\lim\:_{x\to\:0}(\frac{4x^{2}-3x}{x^{2}+0.8x+\frac{4}{x}})
(d^2)/(dx^2)(sqrt(r)+\sqrt[3]{r})	\frac{d^{2}}{dx^{2}}(\sqrt{r}+\sqrt[3]{r})
derivative of ((x+8)/(x-8))^5	derivative\:(\frac{x+8}{x-8})^{5}
derivative of e^xln(x)	derivative\:e^{x}\ln(x)
sum from n=1 to infinity of 1/(n^2+7n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+7n}
derivative of F(x)=(x^4+9x^2-7)^8	derivative\:F(x)=(x^{4}+9x^{2}-7)^{8}
integral from 3 to 9 of 8/x	\int\:_{3}^{9}\frac{8}{x}dx
limit as x approaches 4 of (7+x)/(4-x)	\lim\:_{x\to\:4}(\frac{7+x}{4-x})
limit as x approaches 0 of x/(sin^2(0))	\lim\:_{x\to\:0}(\frac{x}{\sin^{2}(0)})
integral of (tan(2x))/2	\int\:\frac{\tan(2x)}{2}dx
laplacetransform 8t^3	laplacetransform\:8t^{3}
limit as x approaches+0-of (2^x-1)/x	\lim\:_{x\to\:+0-}(\frac{2^{x}-1}{x})
integral of x^5sqrt(8+x^6)	\int\:x^{5}\sqrt{8+x^{6}}dx
integral of (e^x)/(sqrt(1+e^{2x))}	\int\:\frac{e^{x}}{\sqrt{1+e^{2x}}}dx
integral of (2x-1)/(x^2-2x+1)	\int\:\frac{2x-1}{x^{2}-2x+1}dx
derivative of 1/(x^{14})	\frac{d}{dx}(\frac{1}{x^{14}})
derivative of (5-e^{-4x})^4	derivative\:(5-e^{-4x})^{4}
integral from 1 to infinity of 4/(x^2)	\int\:_{1}^{\infty\:}\frac{4}{x^{2}}dx
integral of \sqrt[7]{tan(9x)}sec^2(9x)	\int\:\sqrt[7]{\tan(9x)}\sec^{2}(9x)dx
integral of 2^x+8sinh(x)	\int\:2^{x}+8\sinh(x)dx
integral from 9 to 11 of 2piy(9/y)	\int\:_{9}^{11}2πy(\frac{9}{y})dy
integral of x/(sqrt(x^4+36))	\int\:\frac{x}{\sqrt{x^{4}+36}}dx
integral of (25)/(x^3-27)	\int\:\frac{25}{x^{3}-27}dx
(\partial)/(\partial x)(x^{1/2}y^{1/2}z)	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}\cdot\:y^{\frac{1}{2}}\cdot\:z)
sum from n=1 to infinity of ((n^3))/(3^{n^2)}	\sum\:_{n=1}^{\infty\:}\frac{(n^{3})}{3^{n^{2}}}
(dy)/(dx)=e^{-2y}	\frac{dy}{dx}=e^{-2y}
y^{''}-4y^'+7y=te^t	y^{\prime\:\prime\:}-4y^{\prime\:}+7y=te^{t}
f(x)=(2xln(x)+x^2-1)/(x-1)	f(x)=\frac{2x\ln(x)+x^{2}-1}{x-1}
limit as x approaches 0+of (1+x)^{5/x}	\lim\:_{x\to\:0+}((1+x)^{\frac{5}{x}})
(dy)/(dt)=-3(y-4)	\frac{dy}{dt}=-3(y-4)
integral of 5z^3e^z	\int\:5z^{3}e^{z}dz
tangent of f(x)=8x^3,\at x= 1/2	tangent\:f(x)=8x^{3},\at\:x=\frac{1}{2}
derivative of arctan(cos(θ))	derivative\:\arctan(\cos(θ))
implicit (dy}{dx},y=\frac{-5x)/5+3sqrt(x^3)-4/(5sqrt(x))	implicit\:\frac{dy}{dx},y=\frac{-5x}{5}+3\sqrt{x^{3}}-\frac{4}{5\sqrt{x}}
tangent of y=3x^2-5x+9	tangent\:y=3x^{2}-5x+9
y^{''}+9y=3sec(3x)	y^{\prime\:\prime\:}+9y=3\sec(3x)
derivative of 5xe^{2x}	derivative\:5xe^{2x}
derivative of (x^2/(sqrt(4-x^2-y^2)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{4-x^{2}-y^{2}}})
limit as x approaches 0 of e^x+2x	\lim\:_{x\to\:0}(e^{x}+2x)
sum from k=3 to infinity of 1/(ln(k))	\sum\:_{k=3}^{\infty\:}\frac{1}{\ln(k)}
integral of 1/(xsqrt(1-4ln^2(x)))	\int\:\frac{1}{x\sqrt{1-4\ln^{2}(x)}}dx
tangent of f(x)=(20x)/(x^2-5),\at x=5	tangent\:f(x)=\frac{20x}{x^{2}-5},\at\:x=5
integral of 1/2 sec^2(x)+4x	\int\:\frac{1}{2}\sec^{2}(x)+4xdx
(d^3)/(dx^3)(sqrt(2x+8))	\frac{d^{3}}{dx^{3}}(\sqrt{2x+8})
integral from-5 to 0 of (sqrt(25-x^2))	\int\:_{-5}^{0}(\sqrt{25-x^{2}})dx
y^'=e^{-x}	y^{\prime\:}=e^{-x}
(\partial)/(\partial z)(xy+z^3)	\frac{\partial\:}{\partial\:z}(xy+z^{3})
area y=2sin(x),y=2cos(x)	area\:y=2\sin(x),y=2\cos(x)
area 3x,xsqrt(18^2-x^2)	area\:3x,x\sqrt{18^{2}-x^{2}}
(\partial)/(\partial y)(e^{6xy}*6x)	\frac{\partial\:}{\partial\:y}(e^{6xy}\cdot\:6x)
integral from 0 to 1 of (\sqrt[4]{x}+1)^2	\int\:_{0}^{1}(\sqrt[4]{x}+1)^{2}dx
limit as x approaches 0 of 8/x-8/(x^2+x)	\lim\:_{x\to\:0}(\frac{8}{x}-\frac{8}{x^{2}+x})
integral of x^2-6xx	\int\:x^{2}-6xxdx
(dy)/(dx)=sqrt(14x+y)-14	\frac{dy}{dx}=\sqrt{14x+y}-14
derivative of x^2+y^2-6x-4y-21	\frac{d}{dx}(x^{2}+y^{2}-6x-4y-21)
derivative of (e+5sqrt(x)/(cos(e^{4x))})	\frac{d}{dx}(\frac{e+5\sqrt{x}}{\cos(e^{4x})})
integral of cos^2(x)sin^5(x)	\int\:\cos^{2}(x)\sin^{5}(x)dx
(\partial)/(\partial u)(ln(u^2+v^2+w^2))	\frac{\partial\:}{\partial\:u}(\ln(u^{2}+v^{2}+w^{2}))
limit as x approaches infinity of e^{x-xs}	\lim\:_{x\to\:\infty\:}(e^{x-xs})
derivative of x^2sin(e^x)	derivative\:x^{2}\sin(e^{x})
limit as x approaches infinity of sqrt((9x^3+8x-4)/(3-5x+x^3))	\lim\:_{x\to\:\infty\:}(\sqrt{\frac{9x^{3}+8x-4}{3-5x+x^{3}}})
limit as t approaches infinity of-654e^{-(7t)/(2180)}+654	\lim\:_{t\to\:\infty\:}(-654e^{-\frac{7t}{2180}}+654)
limit as x approaches 10-of 1/(x+10)	\lim\:_{x\to\:10-}(\frac{1}{x+10})
derivative of (4+x)^2	derivative\:(4+x)^{2}
derivative of 1/((1-x^2^{3/2)})	\frac{d}{dx}(\frac{1}{(1-x^{2})^{\frac{3}{2}}})
(\partial)/(\partial y)(3xy-4x^2y)	\frac{\partial\:}{\partial\:y}(3xy-4x^{2}y)
integral from 0 to 3/5 of sqrt(9-25x^2)	\int\:_{0}^{\frac{3}{5}}\sqrt{9-25x^{2}}dx
inverse oflaplace e^{-s}(1/(s^2))	inverselaplace\:e^{-s}(\frac{1}{s^{2}})
integral of sin^2(3x)	\int\:\sin^{2}(3x)dx
integral from-1 to 2 of sqrt(x)	\int\:_{-1}^{2}\sqrt{x}dx
taylor cos(x+pi/2)	taylor\:\cos(x+\frac{π}{2})
integral from-1 to 1 of 1/2 (6-6x^2)^2	\int\:_{-1}^{1}\frac{1}{2}(6-6x^{2})^{2}dx
integral of t(t+1)^6	\int\:t(t+1)^{6}dt
tangent of f(x)=x^2-1,\at x=2	tangent\:f(x)=x^{2}-1,\at\:x=2
area y=e^x,y=e^{2x},x=0,x=ln(2)	area\:y=e^{x},y=e^{2x},x=0,x=\ln(2)
taylor (x-ln(1+x))/(x^2)	taylor\:\frac{x-\ln(1+x)}{x^{2}}
tangent of f(x)=4x^2-4x+1,\at x=0	tangent\:f(x)=4x^{2}-4x+1,\at\:x=0
integral of sqrt(5^2-x^2)	\int\:\sqrt{5^{2}-x^{2}}dx
(\partial)/(\partial x)(xtan(x))	\frac{\partial\:}{\partial\:x}(x\tan(x))
derivative of y=3x(a^2-x^2)	derivative\:y=3x(a^{2}-x^{2})
maclaurin 4(1+e^{-0.3t})	maclaurin\:4(1+e^{-0.3t})
integral of ((ln(x))^3)/(2x)	\int\:\frac{(\ln(x))^{3}}{2x}dx
(\partial)/(\partial x)(cos(x)sin(x))	\frac{\partial\:}{\partial\:x}(\cos(x)\sin(x))
slope of (1/2 ,7),(3,-3/2)	slope\:(\frac{1}{2},7),(3,-\frac{3}{2})
derivative of f(t)=((t^2-4t))/(t+3)	derivative\:f(t)=\frac{(t^{2}-4t)}{t+3}
integral of (2x+3)/(x^2+3x+4)	\int\:\frac{2x+3}{x^{2}+3x+4}dx
limit as x approaches 0+of x^n	\lim\:_{x\to\:0+}(x^{n})
(\partial)/(\partial x)(8xe^{x^2}+y^2)	\frac{\partial\:}{\partial\:x}(8xe^{x^{2}}+y^{2})
limit as x approaches infinity of \sqrt[3]{(5-8x)/(x+3)}	\lim\:_{x\to\:\infty\:}(\sqrt[3]{\frac{5-8x}{x+3}})

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