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Popular Calculus Problems

integral from 1 to 2 of x^5+1/(4x^5)	\int\:_{1}^{2}x^{5}+\frac{1}{4x^{5}}dx
integral from 0 to 1 of (x-4)/(x^2-5x-6)	\int\:_{0}^{1}\frac{x-4}{x^{2}-5x-6}dx
integral of 1/((x^2+1)^3)	\int\:\frac{1}{(x^{2}+1)^{3}}dx
(\partial)/(\partial x)(ln(x^2+xy))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+xy))
(2000)/((2000-P)P)P^'=0.05	\frac{2000}{(2000-P)P}P^{\prime\:}=0.05
laplacetransform 30	laplacetransform\:30
y^{''}+y^'-5x=0	y^{\prime\:\prime\:}+y^{\prime\:}-5x=0
integral from-infinity to x of 1/(x^2)	\int\:_{-\infty\:}^{x}\frac{1}{x^{2}}dx
inverse oflaplace (10)/(s^2+8s+25)	inverselaplace\:\frac{10}{s^{2}+8s+25}
tangent of y=2+1x+10xe^x,\at x=0	tangent\:y=2+1x+10xe^{x},\at\:x=0
y^{''}+y=cos(2x)	y^{\prime\:\prime\:}+y=\cos(2x)
integral of (2-sqrt(x))^2	\int\:(2-\sqrt{x})^{2}dx
3y^{''}-4y^'-4y=0,y(0)=-7,y^'(0)=-8	3y^{\prime\:\prime\:}-4y^{\prime\:}-4y=0,y(0)=-7,y^{\prime\:}(0)=-8
integral of (e^x+x)	\int\:(e^{x}+x)dx
tangent of y=4x^2+5x+1,(0,1)	tangent\:y=4x^{2}+5x+1,(0,1)
derivative of log_{10}(log_{10}(x))	\frac{d}{dx}(\log_{10}(\log_{10}(x)))
integral of sin^2(θ)cos(4θ)	\int\:\sin^{2}(θ)\cos(4θ)dθ
sum from n=1 to infinity of (3n!)/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{3n!}{n^{n}}
integral from 0 to pi/2 of sin(2x)	\int\:_{0}^{\frac{π}{2}}\sin(2x)dx
laplacetransform 3t^4-2t^2+1	laplacetransform\:3t^{4}-2t^{2}+1
laplacetransform cos(sqrt(2)t)	laplacetransform\:\cos(\sqrt{2}t)
derivative of y=sqrt(16-x^2)	derivative\:y=\sqrt{16-x^{2}}
(\partial)/(\partial x)((a-x)^2+b(y-x^2)^2)	\frac{\partial\:}{\partial\:x}((a-x)^{2}+b(y-x^{2})^{2})
integral of sqrt(x^3)ln(\sqrt[3]{x})	\int\:\sqrt{x^{3}}\ln(\sqrt[3]{x})dx
integral of 6x^2y	\int\:6x^{2}ydy
(\partial)/(\partial L)(bL^3{K}(b)(b)^2)	\frac{\partial\:}{\partial\:L}(bL^{3}{K}(b)(b)^{2})
tangent of y=((x^2-1))/((x^2+x+1))	tangent\:y=\frac{(x^{2}-1)}{(x^{2}+x+1)}
derivative of 6x^{3/2}sec(x)	\frac{d}{dx}(6x^{\frac{3}{2}}\sec(x))
x^2y^{''}-xy^'+y=0,y=x	x^{2}y^{\prime\:\prime\:}-xy^{\prime\:}+y=0,y=x
derivative of-0.4x^2+2.2x+4.7	\frac{d}{dx}(-0.4x^{2}+2.2x+4.7)
derivative of e^x(tan(x-x))	\frac{d}{dx}(e^{x}(\tan(x)-x))
limit as x approaches 0 of x/(x+1)	\lim\:_{x\to\:0}(\frac{x}{x+1})
derivative of 2x^3+3x^2-12x+2	derivative\:2x^{3}+3x^{2}-12x+2
integral of (x^2-5x)*e^x	\int\:(x^{2}-5x)\cdot\:e^{x}dx
tangent of y=10xsin(x),(pi/2 ,5pi)	tangent\:y=10x\sin(x),(\frac{π}{2},5π)
integral of 3arctan(sqrt(x))	\int\:3\arctan(\sqrt{x})dx
derivative of sin(sqrt(x^2+1))	\frac{d}{dx}(\sin(\sqrt{x^{2}+1}))
tangent of f(x)= 2/x ,(4, 1/2)	tangent\:f(x)=\frac{2}{x},(4,\frac{1}{2})
derivative of 1+2cos(x)	\frac{d}{dx}(1+2\cos(x))
derivative of e^{x^2-4}+3x+5	\frac{d}{dx}(e^{x^{2}-4}+3x+5)
slope ofintercept (-4,4),(3,-4)	slopeintercept\:(-4,4),(3,-4)
(y^2+yx)dx+(x^2)dy=0	(y^{2}+yx)dx+(x^{2})dy=0
derivative of y=(x-2)^4	derivative\:y=(x-2)^{4}
derivative of cos((2x^2+1^7))	\frac{d}{dx}(\cos((2x^{2}+1)^{7}))
integral of [((1-x)^3)/((x\sqrt[3]{x))}]	\int\:[\frac{(1-x)^{3}}{(x\sqrt[3]{x})}]dx
limit as x approaches pi/4 of cot(x)	\lim\:_{x\to\:\frac{π}{4}}(\cot(x))
integral from 0 to pi/2 of tan(x)	\int\:_{0}^{\frac{π}{2}}\tan(x)dx
integral of (1000x)/(x^2+e)	\int\:\frac{1000x}{x^{2}+e}dx
derivative of (x^2-8x+4)sqrt(25-x^2)	derivative\:(x^{2}-8x+4)\sqrt{25-x^{2}}
limit as x approaches 0 of (3\|x\|)/x	\lim\:_{x\to\:0}(\frac{3\left\|x\right\|}{x})
integral of (x^4ln(x))	\int\:(x^{4}\ln(x))dx
derivative of 50sqrt(x)-5x	\frac{d}{dx}(50\sqrt{x}-5x)
integral of (x^2+1)/((x-10)(x-9)^2)	\int\:\frac{x^{2}+1}{(x-10)(x-9)^{2}}dx
sum from n=1 to infinity of \sqrt[n]{10}	\sum\:_{n=1}^{\infty\:}\sqrt[n]{10}
(x^2+81)((dy)/(dx))=2,y(9)=0	(x^{2}+81)(\frac{dy}{dx})=2,y(9)=0
slope of (x+2)^2+(y-3)^2=37,(4,2)	slope\:(x+2)^{2}+(y-3)^{2}=37,(4,2)
y^'=r-ky	y^{\prime\:}=r-ky
limit as x approaches-1 of x\|x+1\|	\lim\:_{x\to\:-1}(x\left\|x+1\right\|)
derivative of f(x)=7y^7-4y^6+35y^4-24y^2	derivative\:f(x)=7y^{7}-4y^{6}+35y^{4}-24y^{2}
limit as x approaches 0 of (((x^2+3)))/x	\lim\:_{x\to\:0}(\frac{((x^{2}+3))}{x})
tangent of f(x)=(8-9x)(8+9x),\at x=9	tangent\:f(x)=(8-9x)(8+9x),\at\:x=9
limit as x approaches infinity of x^2+2	\lim\:_{x\to\:\infty\:}(x^{2}+2)
integral of sqrt(5-2x+x^2)	\int\:\sqrt{5-2x+x^{2}}dx
(\partial)/(\partial y)((4x-y)/(4x+y))	\frac{\partial\:}{\partial\:y}(\frac{4x-y}{4x+y})
(6+x)y^'=9y	(6+x)y^{\prime\:}=9y
integral of (x+1)/(x^2+2x+4)	\int\:\frac{x+1}{x^{2}+2x+4}dx
derivative of 8^x-14^x	\frac{d}{dx}(8^{x}-14^{x})
(dy)/(dt)=2(t+1)y	\frac{dy}{dt}=2(t+1)y
integral from-1 to 3 of sqrt(1+(2y+2)^2)	\int\:_{-1}^{3}\sqrt{1+(2y+2)^{2}}dy
tangent of x^3,\at x=-2	tangent\:x^{3},\at\:x=-2
derivative of (sqrt(s)-7)/(sqrt(s)+5)	derivative\:\frac{\sqrt{s}-7}{\sqrt{s}+5}
integral of tan(7xse)c^27x	\int\:\tan(7xse)c^{2}7xdx
integral of e^{-2x}cos(3x)	\int\:e^{-2x}\cos(3x)dx
limit as x approaches 3 of sqrt(x^2+16)	\lim\:_{x\to\:3}(\sqrt{x^{2}+16})
(\partial)/(\partial x)(25-5x^2-y^2)	\frac{\partial\:}{\partial\:x}(25-5x^{2}-y^{2})
limit as x approaches infinity of 2x+5	\lim\:_{x\to\:\infty\:}(2x+5)
integral from 0 to pi of 3sin^2(tco)s^4t	\int\:_{0}^{π}3\sin^{2}(tco)s^{4}tdt
derivative of f(x)=(3x^2e^x-4)/(x^2)	derivative\:f(x)=\frac{3x^{2}e^{x}-4}{x^{2}}
limit as x approaches 1-of 2x^4-9x^3+7	\lim\:_{x\to\:1-}(2x^{4}-9x^{3}+7)
((3y)/x-8)dx+3dy=0	(\frac{3y}{x}-8)dx+3dy=0
(\partial)/(\partial x)(\|3x+y-4\|)	\frac{\partial\:}{\partial\:x}(\left\|3x+y-4\right\|)
limit as x approaches 6 of sqrt(36-x^2)	\lim\:_{x\to\:6}(\sqrt{36-x^{2}})
integral from 1 to 2 of x(x^2+1)^2	\int\:_{1}^{2}x(x^{2}+1)^{2}dx
(dv}{dt}=\frac{(10-v))/1	\frac{dv}{dt}=\frac{(10-v)}{1}
integral of 1/(x(x-1)^2)	\int\:\frac{1}{x(x-1)^{2}}dx
integral of sqrt(16-y)	\int\:\sqrt{16-y}dy
integral from 0 to 2 of-10x^3sqrt(x^2+4)	\int\:_{0}^{2}-10x^{3}\sqrt{x^{2}+4}dx
6t(dy)/(dt)+y=t^7	6t\frac{dy}{dt}+y=t^{7}
derivative of 2/(x+2)	derivative\:\frac{2}{x+2}
derivative of f(x)=(-4x^2+16)^2	derivative\:f(x)=(-4x^{2}+16)^{2}
integral from 0 to pi/4 of ln(sec(x))	\int\:_{0}^{\frac{π}{4}}\ln(\sec(x))dx
integral of (8m^2)/((m^3+2)^3)	\int\:\frac{8m^{2}}{(m^{3}+2)^{3}}dm
limit as x approaches 0+of x^{5/x}	\lim\:_{x\to\:0+}(x^{\frac{5}{x}})
limit as x approaches 0 of 3/(10-e^x)	\lim\:_{x\to\:0}(\frac{3}{10-e^{x}})
integral of 2e^2	\int\:2e^{2}
derivative of xlog_{2}(x)	\frac{d}{dx}(x\log_{2}(x))
sum from n=1 to infinity of-1/(8^n)	\sum\:_{n=1}^{\infty\:}-\frac{1}{8^{n}}
integral of (4x^2-x+5)/(12x)	\int\:\frac{4x^{2}-x+5}{12x}dx
integral of (x^5)/(sqrt(x^2+3))	\int\:\frac{x^{5}}{\sqrt{x^{2}+3}}dx
integral from 0 to 4 of (2t+4)	\int\:_{0}^{4}(2t+4)dt

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