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Popular Calculus Problems

sum from n=0 to infinity of (1^n)/(n+2)	\sum\:_{n=0}^{\infty\:}\frac{1^{n}}{n+2}
integral from 0 to 5 of 1/((6-2x)^{1/3)}	\int\:_{0}^{5}\frac{1}{(6-2x)^{\frac{1}{3}}}dx
integral of (x^3-2x)^2(1/x-5)	\int\:(x^{3}-2x)^{2}(\frac{1}{x}-5)dx
derivative of tan(e^{8t})+e^{tan(8t)}	derivative\:\tan(e^{8t})+e^{\tan(8t)}
tangent of f(x)= x/(e^x),\at x=-1	tangent\:f(x)=\frac{x}{e^{x}},\at\:x=-1
y^'=8xe^{(5y)},y(0)=0	y^{\prime\:}=8xe^{(5y)},y(0)=0
derivative of arccot(2x)	\frac{d}{dx}(\arccot(2x))
integral of (7(x^2+5))/(x(x^2+7))	\int\:\frac{7(x^{2}+5)}{x(x^{2}+7)}dx
area 3x^3-x^2-10x,-x^2+2x,[-2,2]	area\:3x^{3}-x^{2}-10x,-x^{2}+2x,[-2,2]
integral from-2 to 0 of 2x^2+5x+6	\int\:_{-2}^{0}2x^{2}+5x+6dx
derivative of f(x)=-3/2 x^3+2/5 x^2-4	derivative\:f(x)=-\frac{3}{2}x^{3}+\frac{2}{5}x^{2}-4
derivative of g(t)= 7/(8t^5)	derivative\:g(t)=\frac{7}{8t^{5}}
integral of 3sin(6x)	\int\:3\sin(6x)dx
(d^2)/(dx^2)(-x/y)	\frac{d^{2}}{dx^{2}}(-\frac{x}{y})
y^{''}+36y=6t^2	y^{\prime\:\prime\:}+36y=6t^{2}
derivative of 5^{x^3}	derivative\:5^{x^{3}}
expand ((k^2-x^2)^3)/(x^2+a^2)	expand\:\frac{(k^{2}-x^{2})^{3}}{x^{2}+a^{2}}
integral of 5x\sqrt[3]{(9-4x^2)^2}	\int\:5x\sqrt[3]{(9-4x^{2})^{2}}dx
integral of sec(x)tan(x)sqrt(1+sec(x))	\int\:\sec(x)\tan(x)\sqrt{1+\sec(x)}dx
f(x)=x\|x\|	f(x)=x\left\|x\right\|
integral from 4 to-2 of 1/2	\int\:_{4}^{-2}\frac{1}{2}dx
x^'=x+3	x^{\prime\:}=x+3
tangent of 9x-6sqrt(x)	tangent\:9x-6\sqrt{x}
derivative of-3x^3	derivative\:-3x^{3}
limit as x approaches 0 of sqrt(x^2-1)	\lim\:_{x\to\:0}(\sqrt{x^{2}-1})
integral of (3x^2+9)^2	\int\:(3x^{2}+9)^{2}dx
f(r)=4pir^2	f(r)=4πr^{2}
tangent of-3x^{1/2}+x^{3/2},\at x=9	tangent\:-3x^{\frac{1}{2}}+x^{\frac{3}{2}},\at\:x=9
derivative of ((x^2+2/3)^2)	\frac{d}{dx}((\frac{x^{2}+2}{3})^{2})
slope of (3,2),(-3,-2)	slope\:(3,2),(-3,-2)
roots Ae^x	roots\:Ae^{x}
derivative of f(x)=sec(x)tan(x)	derivative\:f(x)=\sec(x)\tan(x)
derivative of-4cos(x+sin(x))	\frac{d}{dx}(-4\cos(x)+\sin(x))
tangent of f(x)= x/((4x-3)^8),\at x=1	tangent\:f(x)=\frac{x}{(4x-3)^{8}},\at\:x=1
area 8-2x,x^3-7x^2+12x,1,4	area\:8-2x,x^{3}-7x^{2}+12x,1,4
integral of (x^4+x+1)/(x^3-x)	\int\:\frac{x^{4}+x+1}{x^{3}-x}dx
y^'-y=2x	y^{\prime\:}-y=2x
(\partial)/(\partial z)(2x^2+3y^2-z^2)	\frac{\partial\:}{\partial\:z}(2x^{2}+3y^{2}-z^{2})
derivative of 1/((2x+1)^2)	derivative\:\frac{1}{(2x+1)^{2}}
integral of 1/(x^2sqrt(4x^2-25))	\int\:\frac{1}{x^{2}\sqrt{4x^{2}-25}}dx
derivative of t^2(5t+2)^3	derivative\:t^{2}(5t+2)^{3}
integral of e^{4x-7}	\int\:e^{4x-7}dx
derivative of f(x)=cot^2(x)	derivative\:f(x)=\cot^{2}(x)
integral of e^{0.04x}	\int\:e^{0.04x}dx
y^'+y=2e^{-t}	y^{\prime\:}+y=2e^{-t}
integral from 0 to 2 of te^{-1}	\int\:_{0}^{2}te^{-1}dt
derivative of f(x)=sqrt(5x+x^2)	derivative\:f(x)=\sqrt{5x+x^{2}}
(\partial)/(\partial x)(4ysin(x^2y))	\frac{\partial\:}{\partial\:x}(4y\sin(x^{2}y))
integral from 0 to pi/2 of sin^3(t)	\int\:_{0}^{\frac{π}{2}}\sin^{3}(t)dt
derivative of (3x^2-2/(2x+3))	\frac{d}{dx}(\frac{3x^{2}-2}{2x+3})
integral from 0 to 8 of 2pix(x^{3/2})	\int\:_{0}^{8}2πx(x^{\frac{3}{2}})dx
integral of 8xsec^2(x)	\int\:8x\sec^{2}(x)dx
integral of xsin(2ax)	\int\:x\sin(2ax)dx
derivative of y=(1+6x^2)(x-x^2)	derivative\:y=(1+6x^{2})(x-x^{2})
sum from n=1 to infinity of 5/(n^4)	\sum\:_{n=1}^{\infty\:}\frac{5}{n^{4}}
limit as x approaches infinity of x/(3x)	\lim\:_{x\to\:\infty\:}(\frac{x}{3x})
(d^2)/(dx^2)(1/(4x^2+5x))	\frac{d^{2}}{dx^{2}}(\frac{1}{4x^{2}+5x})
derivative of cos(7-2x)	\frac{d}{dx}(\cos(7-2x))
derivative of e^x(xsin(x+(1-x)cos(x)))	\frac{d}{dx}(e^{x}(x\cdot\:\sin(x)+(1-x)\cdot\:\cos(x)))
(\partial)/(\partial x)(1/(x^7))	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{7}})
integral of cos^2(5y)sin(5y)	\int\:\cos^{2}(5y)\sin(5y)dy
integral from-3 to infinity of e^{-x}	\int\:_{-3}^{\infty\:}e^{-x}dx
taylor 1/(1-x)	taylor\:\frac{1}{1-x}
(\partial)/(\partial z)(-9zcos(3x+yz))	\frac{\partial\:}{\partial\:z}(-9z\cos(3x+yz))
derivative of sqrt(1+x^2+y^2)	\frac{d}{dx}(\sqrt{1+x^{2}+y^{2}})
(dy)/(dx)=2y(1-y)	\frac{dy}{dx}=2y(1-y)
derivative of (x^2+5x+6)/(x^2-4)	derivative\:\frac{x^{2}+5x+6}{x^{2}-4}
derivative of 2/((6x^2+5x+1)^2)	derivative\:\frac{2}{(6x^{2}+5x+1)^{2}}
integral of 1/(aauu)	\int\:\frac{1}{aauu}du
derivative of 1/(sin(x^2))	\frac{d}{dx}(\frac{1}{\sin(x^{2})})
integral of e^{4x}cos(3x)	\int\:e^{4x}\cos(3x)dx
(\partial)/(\partial x)(y+e^x)	\frac{\partial\:}{\partial\:x}(y+e^{x})
integral from 0 to 1 of (2x)/(1+x^4)	\int\:_{0}^{1}\frac{2x}{1+x^{4}}dx
tangent of f(x)=(-4x)/(x^2+1),\at x=0	tangent\:f(x)=\frac{-4x}{x^{2}+1},\at\:x=0
limit as x approaches 3 of (x^2-6)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{2}-6}{x-3})
(d^2)/(dx^2)(2/(3t^4))	\frac{d^{2}}{dx^{2}}(\frac{2}{3t^{4}})
taylor ln(1+2*t),2	taylor\:\ln(1+2\cdot\:t),2
derivative of (4x-1/(x^2))	\frac{d}{dx}(\frac{4x-1}{x^{2}})
(\partial)/(\partial x)(-6y^2+12xy)	\frac{\partial\:}{\partial\:x}(-6y^{2}+12xy)
(\partial}{\partial x}(\frac{(p(q,x)-cq))/x)	\frac{\partial\:}{\partial\:x}(\frac{(p(q,x)-cq)}{x})
(\partial)/(\partial y)(8ze^{xyz})	\frac{\partial\:}{\partial\:y}(8ze^{xyz})
laplacetransform f(t)=4t-10	laplacetransform\:f(t)=4t-10
derivative of (x^5/7)	\frac{d}{dx}(\frac{x^{5}}{7})
derivative of 2xln(x+x^2-1)	\frac{d}{dx}(2x\ln(x)+x^{2}-1)
integral of 3sin^5(x)cos^{-3/2}(x)	\int\:3\sin^{5}(x)\cos^{-\frac{3}{2}}(x)dx
integral of 2/x+3e^x	\int\:\frac{2}{x}+3e^{x}dx
integral of 1/(x(2+3u))	\int\:\frac{1}{x(2+3u)}dx
y^{''}-2y^'+y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+y=0
integral of x(12x+4)	\int\:x(12x+4)dx
limit as x approaches 2 of ln\|2-x\|	\lim\:_{x\to\:2}(\ln\left\|2-x\right\|)
tangent of f(x)=-x^3+9x^2-6x+9,\at x=7	tangent\:f(x)=-x^{3}+9x^{2}-6x+9,\at\:x=7
limit as x approaches-infinity of x/c	\lim\:_{x\to\:-\infty\:}(\frac{x}{c})
integral of 2(2x+8)^5	\int\:2(2x+8)^{5}dx
(\partial)/(\partial x)((x+2)^2(y+3))	\frac{\partial\:}{\partial\:x}((x+2)^{2}(y+3))
integral from 0 to 6 of 1/(sqrt(36-x^2))	\int\:_{0}^{6}\frac{1}{\sqrt{36-x^{2}}}dx
integral of (y+2)	\int\:(y+2)dy
limit as x approaches 3 of (x)+(4-x)	\lim\:_{x\to\:3}((x)+(4-x))
derivative of f(x)=(1-x)/x	derivative\:f(x)=\frac{1-x}{x}
derivative of xsin(xcos(x))	\frac{d}{dx}(x\sin(x)\cos(x))
integral of x^{10}	\int\:x^{10}dx

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