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Popular Calculus Problems

derivative of-sqrt(3)sin(x+cos(x))	\frac{d}{dx}(-\sqrt{3}\sin(x)+\cos(x))
derivative of y=3^{-x^2}	derivative\:y=3^{-x^{2}}
integral of e^{0.2y}	\int\:e^{0.2y}dy
integral of (8x^3+13x)/((x^2+2)^2)	\int\:\frac{8x^{3}+13x}{(x^{2}+2)^{2}}dx
integral from 2 to infinity of 1/(x^2)	\int\:_{2}^{\infty\:}\frac{1}{x^{2}}dx
integral from 1 to 3 of (3x^2-2x+1)	\int\:_{1}^{3}(3x^{2}-2x+1)dx
integral of 16sin^2(θ)	\int\:16\sin^{2}(θ)dθ
derivative of f(x)= A/(x^{14)}+Be^x	derivative\:f(x)=\frac{A}{x^{14}}+Be^{x}
derivative of y=2+sqrt(x-7)	derivative\:y=2+\sqrt{x-7}
limit as x approaches infinity of e^{1/x ln(2^x+3^x+5^x)}	\lim\:_{x\to\:\infty\:}(e^{\frac{1}{x}\ln(2^{x}+3^{x}+5^{x})})
derivative of cos^2(1-2x)	\frac{d}{dx}(\cos^{2}(1-2x))
xy+y^'=166x	xy+y^{\prime\:}=166x
(2xy+2y^2)dx+(x^2+4xy)dy=0,y(1)=1	(2xy+2y^{2})dx+(x^{2}+4xy)dy=0,y(1)=1
integral of 1/(x^2)+1	\int\:\frac{1}{x^{2}}+1dx
sum from n=2 to infinity of 3/(5^n)	\sum\:_{n=2}^{\infty\:}\frac{3}{5^{n}}
derivative of-x^4-4/3 x^3+4x^2	\frac{d}{dx}(-x^{4}-\frac{4}{3}x^{3}+4x^{2})
integral of (sin(x)+2cos(x))	\int\:(\sin(x)+2\cos(x))dx
derivative of x^t	\frac{d}{dx}(x^{t})
integral from 0 to 4 of (2t+4)^{-1/2}	\int\:_{0}^{4}(2t+4)^{-\frac{1}{2}}dt
y^'+2y=y^2	y^{\prime\:}+2y=y^{2}
integral of-2ln(3/2 x)-cos(3x)	\int\:-2\ln(\frac{3}{2}x)-\cos(3x)dx
integral of (xe^x)/(sqrt(1+e^x))	\int\:\frac{xe^{x}}{\sqrt{1+e^{x}}}dx
integral of 7e^{-t}	\int\:7e^{-t}dt
derivative of (1-2e^x/(1-2cos(x)))	\frac{d}{dx}(\frac{1-2e^{x}}{1-2\cos(x)})
(x+1)y^'=x^2-y	(x+1)y^{\prime\:}=x^{2}-y
integral of 9/(x^2+1)	\int\:\frac{9}{x^{2}+1}dx
(x/(1-x))^'	(\frac{x}{1-x})^{\prime\:}
y^{''}-8y^'+20y=200x^2-52xe^x	y^{\prime\:\prime\:}-8y^{\prime\:}+20y=200x^{2}-52xe^{x}
(\partial)/(\partial x)(7x+6y+7xy)	\frac{\partial\:}{\partial\:x}(7x+6y+7xy)
integral of cos(sqrt(7x))	\int\:\cos(\sqrt{7x})dx
area x^2-4x+1,3x-5,1,4	area\:x^{2}-4x+1,3x-5,1,4
integral of (2y-x)/(-(y+xy))	\int\:\frac{2y-x}{-(y+xy)}dx
integral of 5ln(x^2+5)	\int\:5\ln(x^{2}+5)dx
tangent of f(x)=(1+2x)^{12},\at x=0	tangent\:f(x)=(1+2x)^{12},\at\:x=0
4y^{''}+4y^'+17y=0	4y^{\prime\:\prime\:}+4y^{\prime\:}+17y=0
2y^'+y=3t	2y^{\prime\:}+y=3t
(\partial)/(\partial x)(10x+5y)	\frac{\partial\:}{\partial\:x}(10x+5y)
sum from n=1 to infinity}cos(e^{-n of)	\sum\:_{n=1}^{\infty\:}\cos(e^{-n})
integral of x^{(-3)/2}	\int\:x^{\frac{-3}{2}}dx
integral of 2x-8	\int\:2x-8dx
d/(dθ)(3sin(θ))	\frac{d}{dθ}(3\sin(θ))
area y=2x^2,(3,18)	area\:y=2x^{2},(3,18)
integral of x/(sqrt(1-16x^4))	\int\:\frac{x}{\sqrt{1-16x^{4}}}dx
derivative of x/((2x+2*sqrt(x+3)))	derivative\:\frac{x}{(2x+2\cdot\:\sqrt{x+3})}
integral from 0 to 5 of 1/(x^{16/17)}	\int\:_{0}^{5}\frac{1}{x^{\frac{16}{17}}}dx
d/(dθ)(5sin(θ))	\frac{d}{dθ}(5\sin(θ))
limit as x approaches 0 of 1/4 (4)^4	\lim\:_{x\to\:0}(\frac{1}{4}(4)^{4})
integral of tan(3t)	\int\:\tan(3t)dt
y^{'''}+y^{''}=x	y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}=x
integral of 3/(3+e^x)	\int\:\frac{3}{3+e^{x}}dx
y^{''}+y^'-30y=0,y(0)=2,y^'(0)=-2	y^{\prime\:\prime\:}+y^{\prime\:}-30y=0,y(0)=2,y^{\prime\:}(0)=-2
(2x+1)^'	(2x+1)^{\prime\:}
y^'=(y+2x)^2,y(0)=sqrt(3)	y^{\prime\:}=(y+2x)^{2},y(0)=\sqrt{3}
taylor 4x^4+3x^3+2x^2+x+11	taylor\:4x^{4}+3x^{3}+2x^{2}+x+11
derivative of (-1/x)	\frac{d}{dx}(\frac{-1}{x})
(d^2)/(dx^2)((x^2)/(2+x))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{2+x})
(dy)/(dx)-3y=e^{2x}	\frac{dy}{dx}-3\cdot\:y=e^{2\cdot\:x}
derivative of 460(1+x/(x^2+80))	\frac{d}{dx}(460(1+\frac{x}{x^{2}+80}))
integral of (5x-2)/((x-2)^2)	\int\:\frac{5x-2}{(x-2)^{2}}dx
integral of (-3x^2)/(sqrt(4x-x^2))	\int\:\frac{-3x^{2}}{\sqrt{4x-x^{2}}}dx
derivative of 1/27 (9x^2+6^{3/2})	\frac{d}{dx}(\frac{1}{27}(9x^{2}+6)^{\frac{3}{2}})
y^'+9y=t+e^{-5t}	y^{\prime\:}+9y=t+e^{-5t}
(x-y)dx+xdy=0	(x-y)dx+xdy=0
derivative of-4sec(x+2csc(x))	\frac{d}{dx}(-4\sec(x)+2\csc(x))
area (4x)/(x^2+1),(2x)/(25)	area\:\frac{4x}{x^{2}+1},\frac{2x}{25}
integral from 0 to infinity of x^2e^{-x/2}	\int\:_{0}^{\infty\:}x^{2}e^{-\frac{x}{2}}dx
limit as x approaches 0+of sqrt(xe^{sin(pi/x))}	\lim\:_{x\to\:0+}(\sqrt{xe^{\sin(\frac{π}{x})}})
taylor sin(x)pi	taylor\:\sin(x)π
integral of (6ln^2(x))/x	\int\:\frac{6\ln^{2}(x)}{x}dx
integral of (-4x)/((1-2x^2)^2)	\int\:\frac{-4x}{(1-2x^{2})^{2}}dx
taylor ln((1+x)/(1-x)),0	taylor\:\ln(\frac{1+x}{1-x}),0
y^'+xy^2=0	y^{\prime\:}+xy^{2}=0
limit as x approaches 0 of sqrt(x+a)	\lim\:_{x\to\:0}(\sqrt{x+a})
limit as x approaches 3.1 of (5x)/(6-2x)	\lim\:_{x\to\:3.1}(\frac{5x}{6-2x})
(\partial)/(\partial y)(3x^2y^4+3)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{4}+3)
integral of x/(x^4-16)	\int\:\frac{x}{x^{4}-16}dx
integral of sin(\sqrt[3]{x})	\int\:\sin(\sqrt[3]{x})dx
integral from 0 to 5 of 25-x^2	\int\:_{0}^{5}25-x^{2}dx
limit as h approaches 0 of x^2+2x+h-4	\lim\:_{h\to\:0}(x^{2}+2x+h-4)
limit as x approaches 0 of \|x^2\|	\lim\:_{x\to\:0}(\left\|x^{2}\right\|)
(\partial)/(\partial x)(x^3sin(y))	\frac{\partial\:}{\partial\:x}(x^{3}\sin(y))
integral of 1/(x^2)x	\int\:\frac{1}{x^{2}}xdx
derivative of (2x+3y^{10})	\frac{d}{dx}((2x+3y)^{10})
integral of 2cos^3(6x)	\int\:2\cos^{3}(6x)dx
integral of 1/(z^3sqrt(z^2-49))	\int\:\frac{1}{z^{3}\sqrt{z^{2}-49}}dz
derivative of (x+4^{2/3})	\frac{d}{dx}((x+4)^{\frac{2}{3}})
integral of 1/(-y^2+y+20)	\int\:\frac{1}{-y^{2}+y+20}dy
limit as x approaches 2 of (-1)/0	\lim\:_{x\to\:2}(\frac{-1}{0})
tangent of y=(1+5x)^{10},(0,1)	tangent\:y=(1+5x)^{10},(0,1)
derivative of-(2x/((3+x^2)^2))	\frac{d}{dx}(-\frac{2x}{(3+x^{2})^{2}})
integral of ((2x+y+z)/((x+y)(x+z)))	\int\:(\frac{2x+y+z}{(x+y)(x+z)})dx
taylor x^4cos(x^3)	taylor\:x^{4}\cos(x^{3})
(\partial)/(\partial x)(4cos(x^2+y^2))	\frac{\partial\:}{\partial\:x}(4\cos(x^{2}+y^{2}))
laplacetransform e^tcos(6t)	laplacetransform\:e^{t}\cos(6t)
tangent of 5-x^2	tangent\:5-x^{2}
derivative of f(x)=ln(sqrt(x^2+3))	derivative\:f(x)=\ln(\sqrt{x^{2}+3})
derivative of y=(x+1)(sqrt(x)+2)	derivative\:y=(x+1)(\sqrt{x}+2)
integral of cos(200tn)	\int\:\cos(200tn)dt
integral of sin(20x)cos(17x)	\int\:\sin(20x)\cos(17x)dx
x^2y^'=y^2+5xy+4x^2	x^{2}y^{\prime\:}=y^{2}+5xy+4x^{2}

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