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Popular Calculus Problems

integral from 0 to pi/2 of cos^5(x)	\int\:_{0}^{\frac{π}{2}}\cos^{5}(x)dx
tangent of 2x^4+(3x)/5 ,\at x=0	tangent\:2x^{4}+\frac{3x}{5},\at\:x=0
integral from 0 to 1 of (4x^3)/(1+x^4)	\int\:_{0}^{1}\frac{4x^{3}}{1+x^{4}}dx
8y^{''}+34y=0,y(0)=2,y^'(0)=7	8y^{\prime\:\prime\:}+34y=0,y(0)=2,y^{\prime\:}(0)=7
f^'(x)=sin(x)	f^{\prime\:}(x)=\sin(x)
integral from 2 to infinity of xe^{-3x}	\int\:_{2}^{\infty\:}xe^{-3x}dx
d/(dt)(5t^2x)	\frac{d}{dt}(5t^{2}x)
integral of u^4	\int\:u^{4}du
limit as x approaches 0-of (x^2)/3-1/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{3}-\frac{1}{x})
y^{'''}+6y^{''}+45y^'=0	y^{\prime\:\prime\:\prime\:}+6y^{\prime\:\prime\:}+45y^{\prime\:}=0
y-x+xy^'=0	y-x+xy^{\prime\:}=0
integral from 3 to x^3 of t^4	\int\:_{3}^{x^{3}}t^{4}dt
integral from 0 to 2 of sqrt(2x-x^2)	\int\:_{0}^{2}\sqrt{2x-x^{2}}dx
(\partial}{\partial y}(\frac{(2x+y))/z)	\frac{\partial\:}{\partial\:y}(\frac{(2x+y)}{z})
tangent of f(x)= 4/(sqrt(x)),(4,2)	tangent\:f(x)=\frac{4}{\sqrt{x}},(4,2)
derivative of 4e^{4x}	derivative\:4e^{4x}
derivative of 6x+5	derivative\:6x+5
integral from 0 to pi/6 of cos(9x)	\int\:_{0}^{\frac{π}{6}}\cos(9x)dx
integral of (cos(pi/(x^{11)}))/(x^{12)}	\int\:\frac{\cos(\frac{π}{x^{11}})}{x^{12}}dx
integral of r^3sqrt(1-r^2)	\int\:r^{3}\sqrt{1-r^{2}}dr
derivative of \sqrt[3]{(3x/(6x-5)})	\frac{d}{dx}(\sqrt[3]{\frac{3x}{6x-5}})
area y=sqrt(x),y=x^2,y=1	area\:y=\sqrt{x},y=x^{2},y=1
integral of (cos(pi/(x^3)))/(x^4)	\int\:\frac{\cos(\frac{π}{x^{3}})}{x^{4}}dx
derivative of log_{4}(sec^2(5x^3-4x^2))	derivative\:\log_{4}(\sec^{2}(5x^{3}-4x^{2}))
integral from 0 to 30 of 500	\int\:_{0}^{30}500dx
(y^3-1)e^xdx+3y^2(e^x+1)dy=0,y(0)=2	(y^{3}-1)e^{x}dx+3y^{2}(e^{x}+1)dy=0,y(0)=2
tangent of f(x)=2(3x-8)^4-5x+6,\at x=3	tangent\:f(x)=2(3x-8)^{4}-5x+6,\at\:x=3
integral of 9cos^5(x)sin^4(x)	\int\:9\cos^{5}(x)\sin^{4}(x)dx
(\partial)/(\partial x)(2xy+3x-4y+1)	\frac{\partial\:}{\partial\:x}(2xy+3x-4y+1)
(\partial)/(\partial x)(xy^7-x^2y)	\frac{\partial\:}{\partial\:x}(xy^{7}-x^{2}y)
derivative of (x^2/(4x+1))	\frac{d}{dx}(\frac{x^{2}}{4x+1})
derivative of f(x)=(2-x^2)/(3+x^2)	derivative\:f(x)=\frac{2-x^{2}}{3+x^{2}}
sum from n=1 to infinity of arctan(18n)	\sum\:_{n=1}^{\infty\:}\arctan(18n)
sum from n=0 to infinity of (1.1)^n	\sum\:_{n=0}^{\infty\:}(1.1)^{n}
derivative of y=arctan(x^2+1)	derivative\:y=\arctan(x^{2}+1)
integral of 1/((2-x)(3-x))	\int\:\frac{1}{(2-x)(3-x)}dx
limit as x approaches 5 of (x-25)/(x-5)	\lim\:_{x\to\:5}(\frac{x-25}{x-5})
xydx+y^2dy=0	xydx+y^{2}dy=0
derivative of f(x)=x^3-4x+6	derivative\:f(x)=x^{3}-4x+6
derivative of (x^2/(1+e^x))	\frac{d}{dx}(\frac{x^{2}}{1+e^{x}})
integral of (10x^2)/(x^4-1)	\int\:\frac{10x^{2}}{x^{4}-1}dx
sum from n=5 to infinity of (4/5)^n	\sum\:_{n=5}^{\infty\:}(\frac{4}{5})^{n}
integral of 4x^3(4+x^4)^{1/3}	\int\:4x^{3}(4+x^{4})^{\frac{1}{3}}dx
derivative of r/(sqrt(r^2+4))	derivative\:\frac{r}{\sqrt{r^{2}+4}}
x(dy)/(dx)=x^3+4x^3y	x\frac{dy}{dx}=x^{3}+4x^{3}y
sum from n=1 to infinity of (n5^n)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{n5^{n}}{n!}
derivative of 5tan(x)	derivative\:5\tan(x)
derivative of sqrt(x)(x-14)	derivative\:\sqrt{x}(x-14)
limit as x approaches 0 of e^{-x}	\lim\:_{x\to\:0}(e^{-x})
inverse oflaplace (s-1)/(s(s-1)+2)	inverselaplace\:\frac{s-1}{s(s-1)+2}
integral of e^{-(x/2)^2}	\int\:e^{-(\frac{x}{2})^{2}}dx
(\partial)/(\partial y)(3sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:y}(3\sqrt{x^{2}+y^{2}})
tangent of y=(2x+1)^2	tangent\:y=(2x+1)^{2}
(d^3)/(dx^3)(cos(3x))	\frac{d^{3}}{dx^{3}}(\cos(3x))
integral from 1 to infinity of 1/(2^x)	\int\:_{1}^{\infty\:}\frac{1}{2^{x}}dx
tangent of (2x^2+1)^3(x^2-4)^2	tangent\:(2x^{2}+1)^{3}(x^{2}-4)^{2}
integral of (4xy)	\int\:(4xy)dx
integral of 5xcos(5x)	\int\:5x\cos(5x)dx
f(x)=x^2-5x+3	f(x)=x^{2}-5x+3
derivative of e^{-4x}sin(3x)	\frac{d}{dx}(e^{-4x}\sin(3x))
(dy)/(dx)=(1-xy^2)/(2x^2y)	\frac{dy}{dx}=\frac{1-xy^{2}}{2x^{2}y}
(\partial)/(\partial x)(z(2xy))	\frac{\partial\:}{\partial\:x}(z(2xy))
y^'+y-2=0	y^{\prime\:}+y-2=0
limit as x approaches 2 of 2x^2-7x+4	\lim\:_{x\to\:2}(2x^{2}-7x+4)
integral of tan^3(θ)	\int\:\tan^{3}(θ)dθ
derivative of e^{sec(ln(x^2+1)})	\frac{d}{dx}(e^{\sec(\ln(x^{2}+1))})
integral of 4^{-x}	\int\:4^{-x}dx
(\partial)/(\partial x)(ax+by+c)	\frac{\partial\:}{\partial\:x}(ax+by+c)
(\partial)/(\partial x)(-6sin(2x+y))	\frac{\partial\:}{\partial\:x}(-6\sin(2x+y))
integral from 0 to N of e^{-st}sin(4t)	\int\:_{0}^{N}e^{-st}\sin(4t)dt
limit as x approaches-2 of-2x^2+4x-9	\lim\:_{x\to\:-2}(-2x^{2}+4x-9)
y^'=(2x^3)/(y^2),y(2)=1	y^{\prime\:}=\frac{2x^{3}}{y^{2}},y(2)=1
integral from 0 to 5 of piy^3	\int\:_{0}^{5}πy^{3}dy
(\partial)/(\partial x)((200)/((x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{200}{(x^{2}+y^{2})})
inverse oflaplace 2/(2s+1)	inverselaplace\:\frac{2}{2s+1}
tangent of f(x)=x^4,\at x=4	tangent\:f(x)=x^{4},\at\:x=4
limit as x approaches infinity of (ln(x)+x)/(xnx)	\lim\:_{x\to\:\infty\:}(\frac{\ln(x)+x}{xnx})
derivative of f(x)=(3x^2+1)/(x^{3/2)}	derivative\:f(x)=\frac{3x^{2}+1}{x^{\frac{3}{2}}}
integral of e^{i8x}cos(4x)	\int\:e^{i8x}\cos(4x)dx
derivative of f(x)=(x^2-5x)/(x+1)	derivative\:f(x)=\frac{x^{2}-5x}{x+1}
integral of 3x^2sqrt(x^3-5)	\int\:3x^{2}\sqrt{x^{3}-5}dx
derivative of (-x/(x^2+y^2))	\frac{d}{dx}(\frac{-x}{x^{2}+y^{2}})
integral of (6x-15)/(x^2-3x)	\int\:\frac{6x-15}{x^{2}-3x}dx
integral of (2sin(x)+x)	\int\:(2\sin(x)+x)dx
integral of 1/((7-8x))	\int\:\frac{1}{(7-8x)}dx
sum from n=1 to infinity of 99	\sum\:_{n=1}^{\infty\:}99
sum from k=1 to infinity of (-3/4)^{k-1}	\sum\:_{k=1}^{\infty\:}(-\frac{3}{4})^{k-1}
derivative of 1/(sqrt(x)-sqrt(x))	\frac{d}{dx}(\frac{1}{\sqrt{x}}-\sqrt{x})
integral of cos^8(4-x)sin(4-x)	\int\:\cos^{8}(4-x)\sin(4-x)dx
integral of 1/(1-2x^2)	\int\:\frac{1}{1-2x^{2}}dx
tangent of f(x)=x^2-2x,(-2,8)	tangent\:f(x)=x^{2}-2x,(-2,8)
derivative of (x^2-1)/x	derivative\:\frac{x^{2}-1}{x}
derivative of (3x^2-x-4)(-x^2+2)	derivative\:(3x^{2}-x-4)(-x^{2}+2)
limit as x approaches 0 of 6x-ln(6x+1)	\lim\:_{x\to\:0}(6x-\ln(6x+1))
y^{''}+16y=te^tcos(4t)	y^{\prime\:\prime\:}+16y=te^{t}\cos(4t)
derivative of 2/x-x^2+1	\frac{d}{dx}(\frac{2}{x}-x^{2}+1)
integral of x(e^{x^2}-1)	\int\:x(e^{x^{2}}-1)dx
y^{''}-5y^'=25t	y^{\prime\:\prime\:}-5y^{\prime\:}=25t
integral from sqrt(3) to 3 of 6/(9+x^2)	\int\:_{\sqrt{3}}^{3}\frac{6}{9+x^{2}}dx
integral of 3t^3(t^2+4)^5	\int\:3t^{3}(t^{2}+4)^{5}dt

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