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Popular Calculus Problems

d/(dy)(\sqrt[3]{y})	\frac{d}{dy}(\sqrt[3]{y})
integral of (12y^2)/(4y^3+1)	\int\:\frac{12y^{2}}{4y^{3}+1}dy
(\partial)/(\partial x)(sin(8x-3y))	\frac{\partial\:}{\partial\:x}(\sin(8x-3y))
integral of (3x^2+4x+2)/(2(y-1))	\int\:\frac{3x^{2}+4x+2}{2(y-1)}
sum from n=0 to infinity of e^{-3/(n^2)}	\sum\:_{n=0}^{\infty\:}e^{-\frac{3}{n^{2}}}
sum from n=0 to infinity of (1+k/n)^n	\sum\:_{n=0}^{\infty\:}(1+\frac{k}{n})^{n}
integral from 0.5 to 1 of 3/8 (2-x)^2	\int\:_{0.5}^{1}\frac{3}{8}(2-x)^{2}dx
integral from 4 to 5 of (tsqrt(t-4))	\int\:_{4}^{5}(t\sqrt{t-4})dt
integral of 1/(ln(t))	\int\:\frac{1}{\ln(t)}dt
integral of 15+0.55x	\int\:15+0.55xdx
integral of x^{-5/2}	\int\:x^{-\frac{5}{2}}dx
inverse oflaplace (2-3s)/(s^2-3)	inverselaplace\:\frac{2-3s}{s^{2}-3}
area y=(\|x-2\|)^3,y=8-4x	area\:y=(\left\|x-2\right\|)^{3},y=8-4x
limit as x approaches 0 of ((2^x-1))/x	\lim\:_{x\to\:0}(\frac{(2^{x}-1)}{x})
integral of 1/(y^2-y^3)	\int\:\frac{1}{y^{2}-y^{3}}dy
integral of x^3((2x^2+1)/x)	\int\:x^{3}(\frac{2x^{2}+1}{x})dx
derivative of x/(x+3)	derivative\:\frac{x}{x+3}
integral from 0 to 2 of 5^{-x}	\int\:_{0}^{2}5^{-x}dx
xy^'+15y=0	xy^{\prime\:}+15y=0
derivative of sin(3x^3)	\frac{d}{dx}(\sin(3x^{3}))
integral of (2x-13)/(x^2-13x+50)	\int\:\frac{2x-13}{x^{2}-13x+50}dx
y^'+0.564y^2=0	y^{\prime\:}+0.564y^{2}=0
(\partial)/(\partial x)(4xzsin(y))	\frac{\partial\:}{\partial\:x}(4xz\sin(y))
sum from n=2 to infinity of 6/(n^2-1)	\sum\:_{n=2}^{\infty\:}\frac{6}{n^{2}-1}
(\partial)/(\partial y)(cos(xy)+sin(yz))	\frac{\partial\:}{\partial\:y}(\cos(xy)+\sin(yz))
integral of 7/(sqrt(x^3))	\int\:\frac{7}{\sqrt{x^{3}}}dx
derivative of (2xln(x+x^2-1)/(x-1))	\frac{d}{dx}(\frac{2x\ln(x)+x^{2}-1}{x-1})
integral from 1 to e^3 of (ln^5(x^2))/x	\int\:_{1}^{e^{3}}\frac{\ln^{5}(x^{2})}{x}dx
derivative of 35cos(x)	derivative\:35\cos(x)
d/(dt)((1-t^2)/(1+t^2))	\frac{d}{dt}(\frac{1-t^{2}}{1+t^{2}})
limit as x approaches-1 of (x^2-2)/(1-x)	\lim\:_{x\to\:-1}(\frac{x^{2}-2}{1-x})
y^'=4y^2	y^{\prime\:}=4y^{2}
(\partial)/(\partial y)(600-4x+10x^2y)	\frac{\partial\:}{\partial\:y}(600-4x+10x^{2}y)
integral from 1/2 to 2 of 2/x-1/2 x	\int\:_{\frac{1}{2}}^{2}\frac{2}{x}-\frac{1}{2}xdx
integral of (4-32x)/(sqrt(81-16x^2))	\int\:\frac{4-32x}{\sqrt{81-16x^{2}}}dx
limit as x approaches 3 of (9+x)/(3-x)	\lim\:_{x\to\:3}(\frac{9+x}{3-x})
derivative of f(x)=-x^2-3x+4	derivative\:f(x)=-x^{2}-3x+4
y^'+x^2y=1	y^{\prime\:}+x^{2}y=1
maclaurin (-sin(x)2x)/3	maclaurin\:\frac{-\sin(x)2x}{3}
derivative of 3x^9	\frac{d}{dx}(3x^{9})
integral of 1/(12x^5)	\int\:\frac{1}{12x^{5}}dx
limit as x approaches-infinity+of-5x^3	\lim\:_{x\to\:-\infty\:+}(-5x^{3})
derivative of (x^6/(4-x^5))	\frac{d}{dx}(\frac{x^{6}}{4-x^{5}})
derivative of \sqrt[3]{x^8}	\frac{d}{dx}(\sqrt[3]{x^{8}})
integral of e^{2x}sqrt(1+e^{2x)}	\int\:e^{2x}\sqrt{1+e^{2x}}dx
(\partial)/(\partial x)((6y)/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{6y}{(x+y)^{2}})
limit as x approaches-infinity of 2-x	\lim\:_{x\to\:-\infty\:}(2-x)
integral from 1 to 5 of x/(sqrt(2x+1))	\int\:_{1}^{5}\frac{x}{\sqrt{2x+1}}dx
integral of pi(2x-4)^2	\int\:π(2x-4)^{2}dx
(\partial)/(\partial z)(3xy)	\frac{\partial\:}{\partial\:z}(3xy)
integral from 0 to 7 of 8x*\sqrt[3]{x+1}	\int\:_{0}^{7}8x\cdot\:\sqrt[3]{x+1}dx
derivative of f(x)=ln(x+6)	derivative\:f(x)=\ln(x+6)
integral from 0 to 15 of 1000e^{-0.05t}	\int\:_{0}^{15}1000e^{-0.05t}dt
limit as x approaches 1 of 3-3sqrt(x)	\lim\:_{x\to\:1}(3-3\sqrt{x})
y^'+1/6 y=40	y^{\prime\:}+\frac{1}{6}y=40
(\partial)/(\partial y)((x+y+z)^2)	\frac{\partial\:}{\partial\:y}((x+y+z)^{2})
integral of e^{-x}-e^{-3x}	\int\:e^{-x}-e^{-3x}dx
tangent of f(x)=5e^xcos(x),(0,5)	tangent\:f(x)=5e^{x}\cos(x),(0,5)
integral from 0 to 2 of y^{7/2}	\int\:_{0}^{2}y^{\frac{7}{2}}dy
derivative of (5sqrt(x)/x)	\frac{d}{dx}(\frac{5\sqrt{x}}{x})
f(t)=te^{2t}	f(t)=te^{2t}
integral of-x^2-3x	\int\:-x^{2}-3xdx
derivative of f(x)=4x^{5/4}+10x^{3/2}+3x	derivative\:f(x)=4x^{\frac{5}{4}}+10x^{\frac{3}{2}}+3x
integral of x^5sqrt(x^6-1)	\int\:x^{5}\sqrt{x^{6}-1}dx
area x^2+4x+3,y=-1,x=0,[-2,0]	area\:x^{2}+4x+3,y=-1,x=0,[-2,0]
sum from k=1 to infinity of (20)^k	\sum\:_{k=1}^{\infty\:}(20)^{k}
integral from-4 to 4 of \|x-3\|	\int\:_{-4}^{4}\left\|x-3\right\|dx
derivative of f(x)=((x^3)/(x^8+5))^2	derivative\:f(x)=(\frac{x^{3}}{x^{8}+5})^{2}
(dy)/(dx)=x^{1/4}+x^{-3/5}	\frac{dy}{dx}=x^{\frac{1}{4}}+x^{-\frac{3}{5}}
integral from 1/3 to 5 of 10xln(3x)	\int\:_{\frac{1}{3}}^{5}10x\ln(3x)dx
integral from 0 to 2pi of x^2cos(nx)	\int\:_{0}^{2π}x^{2}\cos(nx)dx
integral of (ln(22x))/x	\int\:\frac{\ln(22x)}{x}dx
integral of x^3sqrt(1+9x^4)	\int\:x^{3}\sqrt{1+9x^{4}}dx
inverse oflaplace (-3s-4)/(2(s^2+2s+2))	inverselaplace\:\frac{-3s-4}{2(s^{2}+2s+2)}
inverse oflaplace (e^{-8s})/s	inverselaplace\:\frac{e^{-8s}}{s}
derivative of e^{2e^x}	\frac{d}{dx}(e^{2e^{x}})
integral of ((csc(y))^2-sec(y)tan(y))	\int\:((\csc(y))^{2}-\sec(y)\tan(y))dy
integral from-pi to pi of x^2sin(x)	\int\:_{-π}^{π}x^{2}\sin(x)dx
(4xy+3y^2-x)dx+x(x+2y)dy=0	(4xy+3y^{2}-x)dx+x(x+2y)dy=0
integral of 2xe^{x^2}	\int\:2xe^{x^{2}}dx
taylor 1/((1+x)^2),0	taylor\:\frac{1}{(1+x)^{2}},0
integral from-6 to 0 of (y/6+sqrt(y+7))	\int\:_{-6}^{0}(\frac{y}{6}+\sqrt{y+7})dy
integral of+1/(1-3y)	\int\:+\frac{1}{1-3y}dy
sum from n=0 to infinity of (4/7)^{n/2}	\sum\:_{n=0}^{\infty\:}(\frac{4}{7})^{\frac{n}{2}}
integral of x^2e^{-3x}	\int\:x^{2}e^{-3x}dx
integral of (4x^2-5)^28x	\int\:(4x^{2}-5)^{2}8xdx
integral from 0 to y of e^{-x}	\int\:_{0}^{y}e^{-x}dx
integral of (x+3)ln(x)	\int\:(x+3)\ln(x)dx
integral of sin(pi)t	\int\:\sin(π)tdt
x^2y*(dy)/(dx)-9=0	x^{2}y\cdot\:\frac{dy}{dx}-9=0
x^{''}-x^'+x=0	x^{\prime\:\prime\:}-x^{\prime\:}+x=0
area x=y^2-5,x=3-y^2	area\:x=y^{2}-5,x=3-y^{2}
derivative of arcsin(ln(x))	derivative\:\arcsin(\ln(x))
f(x)=5+4x-x^3	f(x)=5+4x-x^{3}
sum from n=0 to infinity of (-1)^n(n^3)	\sum\:_{n=0}^{\infty\:}(-1)^{n}(n^{3})
(\partial)/(\partial x)(x^8y^8-x^7y^7)	\frac{\partial\:}{\partial\:x}(x^{8}y^{8}-x^{7}y^{7})
(\partial)/(\partial x)(sinh(x))	\frac{\partial\:}{\partial\:x}(\sinh(x))
integral of 10cos(sqrt(3x))	\int\:10\cos(\sqrt{3x})dx
derivative of (x^2/4*sin(x-2))	\frac{d}{dx}(\frac{x^{2}}{4}\cdot\:\sin(x-2))
integral of x^4(x^2-3x)^2	\int\:x^{4}(x^{2}-3x)^{2}dx

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