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Popular Calculus Problems

integral of 1/(x^2-8x+20)	\int\:\frac{1}{x^{2}-8x+20}dx
integral of e^{-sx}	\int\:e^{-sx}dx
derivative of (x^4/8+(x^{-2})/4)	\frac{d}{dx}(\frac{x^{4}}{8}+\frac{x^{-2}}{4})
derivative of (x^2+x+1/(2sqrt(x)))	\frac{d}{dx}(\frac{x^{2}+x+1}{2\sqrt{x}})
(dy)/(dx)=2x+y,y(0)=4	\frac{dy}{dx}=2x+y,y(0)=4
derivative of 6e^{-8x}	\frac{d}{dx}(6e^{-8x})
tangent of f(x)=sqrt(2x+1),(4,3)	tangent\:f(x)=\sqrt{2x+1},(4,3)
derivative of (x^3-4x)(2x^2+5x)	derivative\:(x^{3}-4x)(2x^{2}+5x)
integral of e^{t(a-s)}	\int\:e^{t(a-s)}dt
integral from 0 to 1 of cos^2(3pix)	\int\:_{0}^{1}\cos^{2}(3πx)dx
(\partial)/(\partial z)(3x^{y/z})	\frac{\partial\:}{\partial\:z}(3x^{\frac{y}{z}})
derivative of e^x((2x+5)^2)/(x-2)	derivative\:e^{x}\frac{(2x+5)^{2}}{x-2}
y^'=-2y+x	y^{\prime\:}=-2y+x
derivative of 3sin^3(x)	derivative\:3\sin^{3}(x)
taylor ln(-3x)+2	taylor\:\ln(-3x)+2
(\partial)/(\partial x)(e^0)	\frac{\partial\:}{\partial\:x}(e^{0})
integral of (7x)/(e^x)	\int\:\frac{7x}{e^{x}}dx
slope of y=sin(xy)+pi,(1,pi)	slope\:y=\sin(xy)+π,(1,π)
tangent of f(x)=x^4+3e^x,\at x=0	tangent\:f(x)=x^{4}+3e^{x},\at\:x=0
integral of 42x(x+7)^5	\int\:42x(x+7)^{5}dx
y^'=3y^2+xy^2,y(0)=1	y^{\prime\:}=3y^{2}+xy^{2},y(0)=1
integral of e^t(sin(t)+cos(t))	\int\:e^{t}(\sin(t)+\cos(t))dt
integral of 1/(4sin(x)-3cos(x))	\int\:\frac{1}{4\sin(x)-3\cos(x)}dx
integral from 1 to infinity of 1/(x^0)	\int\:_{1}^{\infty\:}\frac{1}{x^{0}}dx
(1-2/y+x)(dy)/(dx)+y=2x-1	(1-\frac{2}{y}+x)\frac{dy}{dx}+y=2x-1
integral from-1 to 1 of (e^x)^2	\int\:_{-1}^{1}(e^{x})^{2}dx
integral of 1/(5-x^2)	\int\:\frac{1}{5-x^{2}}dx
inverse oflaplace 1/(s^2-4s+4)	inverselaplace\:\frac{1}{s^{2}-4s+4}
derivative of 2/(xy)	\frac{d}{dx}(\frac{2}{xy})
f^'(x)=x^2e^{x^2}	f^{\prime\:}(x)=x^{2}e^{x^{2}}
tangent of (3x)/(x+1)	tangent\:\frac{3x}{x+1}
derivative of 2x^2-1/16 ln(x)	derivative\:2x^{2}-\frac{1}{16}\ln(x)
y=8in^x+c	y=8in^{x}+c
limit as t approaches 0+of arctan(1/t)	\lim\:_{t\to\:0+}(\arctan(\frac{1}{t}))
integral of (4cos(θ))^2	\int\:(4\cos(θ))^{2}dθ
(\partial)/(\partial t)(e^{sin(x+ct)})	\frac{\partial\:}{\partial\:t}(e^{\sin(x+ct)})
y^{''}+4y^'+4y=x^{-1/2}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=x^{-\frac{1}{2}}
integral of 2cos(x)sin(x)	\int\:2\cos(x)\sin(x)dx
integral of (2x^3+2x-3)	\int\:(2x^{3}+2x-3)dx
(\partial)/(\partial x)(9xcos(x)cos(y))	\frac{\partial\:}{\partial\:x}(9x\cos(x)\cos(y))
integral of log_{e}(2x)	\int\:\log_{e}(2x)dx
derivative of (x-1)^{2/3}	derivative\:(x-1)^{\frac{2}{3}}
(\partial)/(\partial x)(x/y-y/z)	\frac{\partial\:}{\partial\:x}(\frac{x}{y}-\frac{y}{z})
derivative of 81sin(3x)	\frac{d}{dx}(81\sin(3x))
integral of 2x^2-3x+5	\int\:2x^{2}-3x+5dx
(dy}{dt}+\frac{23y)/t = 1/t	\frac{dy}{dt}+\frac{23y}{t}=\frac{1}{t}
area 1390-34x,88x,[11.3934400000000…,12.3934400000000…]	area\:1390-34x,88x,[11.3934400000000…,12.3934400000000…]
(\partial)/(\partial x)(xy^2e^y)	\frac{\partial\:}{\partial\:x}(xy^{2}e^{y})
y^{''}-4y^'+8=0	y^{\prime\:\prime\:}-4y^{\prime\:}+8=0
integral of 1/(1+z^2)	\int\:\frac{1}{1+z^{2}}dz
t^2y^{''}+13ty^'+36y=0	t^{2}y^{\prime\:\prime\:}+13ty^{\prime\:}+36y=0
9y^{''}-60y^'+51y=0,y(0)=1,y^'(0)=0	9y^{\prime\:\prime\:}-60y^{\prime\:}+51y=0,y(0)=1,y^{\prime\:}(0)=0
derivative of (sin(2x+1)^2)	\frac{d}{dx}((\sin(2x)+1)^{2})
tangent of y=x^2-1,(-2,3)	tangent\:y=x^{2}-1,(-2,3)
tangent of f(x)=4x^2-4x+1,\at x=4	tangent\:f(x)=4x^{2}-4x+1,\at\:x=4
derivative of f(x)=sqrt(x/(x+3))	derivative\:f(x)=\sqrt{\frac{x}{x+3}}
sum from n=1 to infinity}((-1)^{n+1 of 2n)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{n+1}2n}{n+1}
integral from-pi/4 to 0 of 6sec^3(x)	\int\:_{-\frac{π}{4}}^{0}6\sec^{3}(x)dx
limit as x approaches 2-of (\|x-2\|)/(x-2)	\lim\:_{x\to\:2-}(\frac{\left\|x-2\right\|}{x-2})
(\partial)/(\partial x)((18xy)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{18xy}{x+y})
limit as x approaches 8 of 15	\lim\:_{x\to\:8}(15)
integral of sin(x)ln(sin(x))	\int\:\sin(x)\ln(\sin(x))dx
tangent of x^6,\at x=3	tangent\:x^{6},\at\:x=3
limit as x approaches 0 of x/(sqrt(x)-1)	\lim\:_{x\to\:0}(\frac{x}{\sqrt{x}-1})
derivative of (cos(x))/(x^4)	derivative\:\frac{\cos(x)}{x^{4}}
derivative of sqrt(5x+7)	\frac{d}{dx}(\sqrt{5x+7})
derivative of (ln(x))/(sqrt(x))	derivative\:\frac{\ln(x)}{\sqrt{x}}
integral from 0 to 1 of x\sqrt[3]{1-x}	\int\:_{0}^{1}x\sqrt[3]{1-x}dx
integral of 1/((1+e^{-x))}	\int\:\frac{1}{(1+e^{-x})}dx
(\partial)/(\partial x)(sin(x/2))	\frac{\partial\:}{\partial\:x}(\sin(\frac{x}{2}))
integral from 1 to 4 of x^2-2x+3	\int\:_{1}^{4}x^{2}-2x+3dx
(dy)/(dx)=((y^2+3xy+x^2))/(x^2)	\frac{dy}{dx}=\frac{(y^{2}+3xy+x^{2})}{x^{2}}
derivative of sqrt((2-x^3))	\frac{d}{dx}(\sqrt{(2-x)^{3}})
integral of-1/(2x)	\int\:-\frac{1}{2x}dx
limit as x approaches pi/3-of cot(3x)	\lim\:_{x\to\:\frac{π}{3}-}(\cot(3x))
tangent of f(x)=x^2-4,(3,5)	tangent\:f(x)=x^{2}-4,(3,5)
derivative of 2x^6-5x^{-1/2}	\frac{d}{dx}(2x^{6}-5x^{-\frac{1}{2}})
derivative of sin^2(pit)	derivative\:\sin^{2}(πt)
sum from n=1 to infinity of n	\sum\:_{n=1}^{\infty\:}n
integral from-infinity to 0 of 1/(4-7x)	\int\:_{-\infty\:}^{0}\frac{1}{4-7x}dx
derivative of e^{x-2}-(sqrt(x))/2	derivative\:e^{x-2}-\frac{\sqrt{x}}{2}
limit as x approaches-2-of 1/(x^2-4)	\lim\:_{x\to\:-2-}(\frac{1}{x^{2}-4})
integral of 1/(e^xcos^2(e^{-x))}	\int\:\frac{1}{e^{x}\cos^{2}(e^{-x})}dx
integral from 0 to infinity of e^{-0.5x}	\int\:_{0}^{\infty\:}e^{-0.5x}dx
integral of (cos(sqrt(x)))/(2sqrt(x))	\int\:\frac{\cos(\sqrt{x})}{2\sqrt{x}}dx
2xydy+(x^2-y^2)dx=0	2xydy+(x^{2}-y^{2})dx=0
integral of xcos(ax^2)	\int\:x\cos(ax^{2})dx
integral from 0 to infinity of 14e^{-7x}	\int\:_{0}^{\infty\:}14e^{-7x}dx
derivative of 8x-3	derivative\:8x-3
integral of (2x-5)(x-3)^9	\int\:(2x-5)(x-3)^{9}dx
integral of cot^3(11x)	\int\:\cot^{3}(11x)dx
integral of tan^5(pix)sec^4(pix)	\int\:\tan^{5}(πx)\sec^{4}(πx)dx
derivative of x^4+7x^2-x	derivative\:x^{4}+7x^{2}-x
integral of 2x^3(3x^4-5)	\int\:2x^{3}(3x^{4}-5)dx
area x=7y, 1/3 y=x, 1/7 y=x	area\:x=7y,\frac{1}{3}y=x,\frac{1}{7}y=x
derivative of ln(sqrt(1+sin^2(x)))	\frac{d}{dx}(\ln(\sqrt{1+\sin^{2}(x)}))
limit as x approaches-7 of (x^2-8)/(7-x)	\lim\:_{x\to\:-7}(\frac{x^{2}-8}{7-x})
derivative of-cos(xsin(x))	\frac{d}{dx}(-\cos(x)\sin(x))
integral of e^{2x}cos(2x)	\int\:e^{2x}\cos(2x)dx
derivative of arctanh(sin(x))	\frac{d}{dx}(\arctanh(\sin(x)))

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