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Popular Calculus Problems

integral of (sqrt(t)+cos(t))	\int\:(\sqrt{t}+\cos(t))dt
d/(dy)(2x+y)	\frac{d}{dy}(2x+y)
integral of 1/((arcsin(y))sqrt(1-y^2))	\int\:\frac{1}{(\arcsin(y))\sqrt{1-y^{2}}}dy
derivative of 3e^{9x}	\frac{d}{dx}(3e^{9x})
integral of e^{t/2}cos(2t)	\int\:e^{\frac{t}{2}}\cos(2t)dt
integral of (e^{-x^2})/(x^2)	\int\:\frac{e^{-x^{2}}}{x^{2}}dx
slope of (20.8)(9.16)	slope\:(20.8)(9.16)
integral of 20x^3+12x^2+6	\int\:20x^{3}+12x^{2}+6dx
integral of cos^3(x)ln(sin(x))	\int\:\cos^{3}(x)\ln(\sin(x))dx
derivative of f(x)=(3x+2)/(3x-2)	derivative\:f(x)=\frac{3x+2}{3x-2}
derivative of sqrt(3x+2y)	\frac{d}{dx}(\sqrt{3x+2y})
limit as x approaches 2 of (2-x)/(x^2-4)	\lim\:_{x\to\:2}(\frac{2-x}{x^{2}-4})
(\partial)/(\partial x)(1/(x+y^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{x+y^{2}})
(\partial)/(\partial y)((x^3-y^2)^{-1})	\frac{\partial\:}{\partial\:y}((x^{3}-y^{2})^{-1})
integral of (x+1)5^{(x+1)^2}	\int\:(x+1)5^{(x+1)^{2}}dx
derivative of e^x-3x^2	\frac{d}{dx}(e^{x}-3x^{2})
derivative of sqrt(25+x^2)	\frac{d}{dx}(\sqrt{25+x^{2}})
xy^2-y^'x^2=0	xy^{2}-y^{\prime\:}x^{2}=0
integral of (3/(x^3)+2x^{3/2}-1)	\int\:(\frac{3}{x^{3}}+2x^{\frac{3}{2}}-1)dx
limit as x approaches 0 of (e^{3x}-e^{-3x})/(4x)	\lim\:_{x\to\:0}(\frac{e^{3x}-e^{-3x}}{4x})
derivative of x^3-15x^2+72x+12	derivative\:x^{3}-15x^{2}+72x+12
derivative of 1/(1/x)	\frac{d}{dx}(\frac{1}{\frac{1}{x}})
integral from 0 to 3 of 2piy(9-y^2)	\int\:_{0}^{3}2πy(9-y^{2})dy
slope of (2,-2),(9,3)	slope\:(2,-2),(9,3)
y^{(1/2)}y^'+y^{(3/2)}=1	y^{(\frac{1}{2})}y^{\prime\:}+y^{(\frac{3}{2})}=1
derivative of 4arcsin(x^2)	derivative\:4\arcsin(x^{2})
integral from 0 to 6 of 1/(x^2-6x+5)	\int\:_{0}^{6}\frac{1}{x^{2}-6x+5}dx
derivative of Ate^{-t}	\frac{d}{dx}(Ate^{-t})
f(x)=e^{x^6}	f(x)=e^{x^{6}}
(\partial)/(\partial y)(3y^2)	\frac{\partial\:}{\partial\:y}(3y^{2})
derivative of (3/x ^{14})	\frac{d}{dx}((\frac{3}{x})^{14})
t^2y^{''}+5ty^'-45y=0	t^{2}y^{\prime\:\prime\:}+5ty^{\prime\:}-45y=0
((xdy-ydx))/(x^2+y^2)=0	\frac{(xdy-ydx)}{x^{2}+y^{2}}=0
integral of-2e^{8x}	\int\:-2e^{8x}dx
derivative of ln^2(x+3)	\frac{d}{dx}(\ln^{2}(x+3))
derivative of 1/(xy)	derivative\:\frac{1}{xy}
f^'(θ)=θcos(θ)sin(θ)	f^{\prime\:}(θ)=θ\cos(θ)\sin(θ)
y^{''}+8y^'+32y=128,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+8y^{\prime\:}+32y=128,y(0)=0,y^{\prime\:}(0)=0
d/(dt)(xy(t){z}(t))	\frac{d}{dt}(xy(t){z}(t))
y^'+tan(x)y= 1/(cos(x))	y^{\prime\:}+\tan(x)y=\frac{1}{\cos(x)}
integral from 1 to 2 of 3x^{-2}	\int\:_{1}^{2}3x^{-2}dx
limit as x approaches 0-of ln\|x\|	\lim\:_{x\to\:0-}(\ln\left\|x\right\|)
(dy)/(dx)+11y=4	\frac{dy}{dx}+11y=4
integral of 1/(sqrt(5-2x^2))	\int\:\frac{1}{\sqrt{5-2x^{2}}}dx
integral of x^2e^{9x}	\int\:x^{2}e^{9x}dx
derivative of x^4+8	\frac{d}{dx}(x^{4}+8)
limit as x approaches-infinity of 5+x^2	\lim\:_{x\to\:-\infty\:}(5+x^{2})
(dy)/(dx)=xy	\frac{dy}{dx}=xy
y^{''}+4y+8=0,y(0)=4,y^'(0)=-3	y^{\prime\:\prime\:}+4y+8=0,y(0)=4,y^{\prime\:}(0)=-3
tangent of f(x)=-2*sqrt(x),\at x=1	tangent\:f(x)=-2\cdot\:\sqrt{x},\at\:x=1
derivative of (6x^2+6x+2/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+6x+2}{\sqrt{x}})
(\partial)/(\partial x)(cos^4(x^3y^8))	\frac{\partial\:}{\partial\:x}(\cos^{4}(x^{3}y^{8}))
f(x)=arctan(sqrt(x))	f(x)=\arctan(\sqrt{x})
derivative of y=x^{4cos(x)}	derivative\:y=x^{4\cos(x)}
(\partial)/(\partial x)(cos^4(x^6y^5))	\frac{\partial\:}{\partial\:x}(\cos^{4}(x^{6}y^{5}))
tangent of y=2x^2+6x+5	tangent\:y=2x^{2}+6x+5
limit as x approaches-1 of 2/(x^3-1)	\lim\:_{x\to\:-1}(\frac{2}{x^{3}-1})
integral from 1 to sqrt(3 of)x4^{x^2}	\int\:_{1}^{\sqrt{3}}x4^{x^{2}}dx
integral of (sqrt(1-x^2))/(x^4)arcsin(x)	\int\:\frac{\sqrt{1-x^{2}}}{x^{4}}\arcsin(x)dx
(\partial)/(\partial t)(sin(2t))	\frac{\partial\:}{\partial\:t}(\sin(2t))
(d^3y)/(dx^3)+(d^2y)/(dx^2)-2y=0	\frac{d^{3}y}{dx^{3}}+\frac{d^{2}y}{dx^{2}}-2y=0
tangent of f(x)=5x^2-2x	tangent\:f(x)=5x^{2}-2x
integral of 1/(16+y^2)	\int\:\frac{1}{16+y^{2}}dy
integral of 11sec^2(x)	\int\:11\sec^{2}(x)dx
integral from 0 to pi of 9sin^2(2x)	\int\:_{0}^{π}9\sin^{2}(2x)dx
area y=x^2-30,y=10-3x	area\:y=x^{2}-30,y=10-3x
(\partial)/(\partial x)(5x^5y^4+7x^6y^8)	\frac{\partial\:}{\partial\:x}(5x^{5}y^{4}+7x^{6}y^{8})
derivative of (7sqrt(x)/8)	\frac{d}{dx}(\frac{7\sqrt{x}}{8})
sum from n=2 to infinity of (2/pi)^n	\sum\:_{n=2}^{\infty\:}(\frac{2}{π})^{n}
derivative of ((-2x+4^7)/((3x-5)^5))	\frac{d}{dx}(\frac{(-2x+4)^{7}}{(3x-5)^{5}})
taylor ln(1+x^3)	taylor\:\ln(1+x^{3})
(dx)/(dt)=x^2e^{-2t},x(0)=3	\frac{dx}{dt}=x^{2}e^{-2t},x(0)=3
tangent of f(x)= 1/(sqrt(9x)),\at x=9	tangent\:f(x)=\frac{1}{\sqrt{9x}},\at\:x=9
integral of cos(pi/x)	\int\:\cos(\frac{π}{x})dx
derivative of f(x)=sqrt(x)(2x+2)	derivative\:f(x)=\sqrt{x}(2x+2)
limit as x approaches 1 of (5-x^2)/(1+x)	\lim\:_{x\to\:1}(\frac{5-x^{2}}{1+x})
integral of 0.1	\int\:0.1
derivative of f(x)=4e^{x^{-3}}	derivative\:f(x)=4e^{x^{-3}}
(\partial)/(\partial y)(sin(2x+3y))	\frac{\partial\:}{\partial\:y}(\sin(2x+3y))
sum from n=0 to infinity of (pi/3)^n	\sum\:_{n=0}^{\infty\:}(\frac{π}{3})^{n}
limit as x approaches 0 of (tan(x))/x	\lim\:_{x\to\:0}(\frac{\tan(x)}{x})
slope of (-1,4),(-3,-1)	slope\:(-1,4),(-3,-1)
simplify log_{2}(4sqrt(x))	simplify\:\log_{2}(4\sqrt{x})
(\partial)/(\partial y)(tan(xy^2))	\frac{\partial\:}{\partial\:y}(\tan(xy^{2}))
integral of cos^3(x)sin(2x)	\int\:\cos^{3}(x)\sin(2x)dx
tangent of f(x)=x^4-5x^3+2,\at x=2	tangent\:f(x)=x^{4}-5x^{3}+2,\at\:x=2
derivative of 5ln(x^3)	\frac{d}{dx}(5\ln(x^{3}))
sum from n=0 to infinity of 1/((2n!))	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n!)}
integral of xcos(mpix)	\int\:x\cos(mπx)dx
(\partial)/(\partial x)(9xe^{6xy})	\frac{\partial\:}{\partial\:x}(9xe^{6xy})
laplacetransform e^{5(t)}	laplacetransform\:e^{5(t)}
(3x+2y+1)dx-(3x+2y-1)dy=0	(3x+2y+1)dx-(3x+2y-1)dy=0
f(t)=t-2	f(t)=t-2
inverse oflaplace 2/(s(s+3))	inverselaplace\:\frac{2}{s(s+3)}
integral of (x+2+3/x)	\int\:(x+2+\frac{3}{x})dx
integral from 4 to infinity of e^{-6x}	\int\:_{4}^{\infty\:}e^{-6x}dx
tangent of 7x^2-12x+6	tangent\:7x^{2}-12x+6
integral of cos(x/8)	\int\:\cos(\frac{x}{8})dx
integral from 0 to pi of sec^2(x/3)	\int\:_{0}^{π}\sec^{2}(\frac{x}{3})dx
(dy)/(dx)=(2x(y-2))/(x^2+1)	\frac{dy}{dx}=\frac{2x(y-2)}{x^{2}+1}

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