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Popular Calculus Problems

integral from 0 to infinity of x^2e^{-x}	\int\:_{0}^{\infty\:}x^{2}e^{-x}dx
slope of (3.5)(2.6)	slope\:(3.5)(2.6)
derivative of sqrt({g)(x(x)^2(x)+x})	\frac{d}{dx}(\sqrt{{g}(x)(x)^{2}(x)+x})
(\partial)/(\partial y)(xy^2+x)	\frac{\partial\:}{\partial\:y}(xy^{2}+x)
limit as x approaches 0 of x^6cos(9/x)	\lim\:_{x\to\:0}(x^{6}\cos(\frac{9}{x}))
limit as x approaches-infinity of 5x^3	\lim\:_{x\to\:-\infty\:}(5x^{3})
(\partial)/(\partial x)((x^{0.5}+y^{0.5})^2)	\frac{\partial\:}{\partial\:x}((x^{0.5}+y^{0.5})^{2})
integral of 7u^7sqrt(u^8+7)	\int\:7u^{7}\sqrt{u^{8}+7}du
limit as x approaches 0+of 5/(x-x^2)	\lim\:_{x\to\:0+}(\frac{5}{x-x^{2}})
limit as x approaches pi/2 of sin(1/x)	\lim\:_{x\to\:\frac{π}{2}}(\sin(\frac{1}{x}))
area 7x^2,x^2+1	area\:7x^{2},x^{2}+1
integral of e^xsqrt(3+e^x)	\int\:e^{x}\sqrt{3+e^{x}}dx
(\partial)/(\partial y)(sin(x)+x^2e^y-1)	\frac{\partial\:}{\partial\:y}(\sin(x)+x^{2}e^{y}-1)
derivative of (6x/(5-cot(x)))	\frac{d}{dx}(\frac{6x}{5-\cot(x)})
integral of 1/(2+sin(x)+3cos(x))	\int\:\frac{1}{2+\sin(x)+3\cos(x)}dx
derivative of sqrt(2x^2+2y^2)	\frac{d}{dx}(\sqrt{2x^{2}+2y^{2}})
integral from-2 to 4 of 10+4x-3x^3	\int\:_{-2}^{4}10+4x-3x^{3}dx
integral of x-x/(x^2+1)	\int\:x-\frac{x}{x^{2}+1}dx
integral of (5x+1)/(6x^2+7x-3)	\int\:\frac{5x+1}{6x^{2}+7x-3}dx
integral of sqrt(sin(x)+1)	\int\:\sqrt{\sin(x)+1}dx
integral of 1/((4x^2+9)^{3/2)}	\int\:\frac{1}{(4x^{2}+9)^{\frac{3}{2}}}dx
sum from n=0 to infinity of 1+2+3+4+5	\sum\:_{n=0}^{\infty\:}1+2+3+4+5
derivative of (e^{arctan(x})/(x^2+1))	\frac{d}{dx}(\frac{e^{\arctan(x)}}{x^{2}+1})
integral of (x/2+1)	\int\:(\frac{x}{2}+1)dx
derivative of cos(pi/2-3x)	\frac{d}{dx}(\cos(\frac{π}{2}-3x))
(\partial)/(\partial x)((4x-2y)/(3x^2+2y))	\frac{\partial\:}{\partial\:x}(\frac{4x-2y}{3x^{2}+2y})
(dy)/(dx)=(-2xy+1)/(x^2+2y)	\frac{dy}{dx}=\frac{-2xy+1}{x^{2}+2y}
tangent of-7/2 x^2+5x+5	tangent\:-\frac{7}{2}x^{2}+5x+5
integral of x^{b-1}e^{x^b}	\int\:x^{b-1}e^{x^{b}}dx
integral of 200-4t	\int\:200-4tdt
derivative of log_{10}((2x/(1+x^2)))	\frac{d}{dx}(\log_{10}(\frac{2x}{1+x^{2}}))
derivative of e^{ax^4}	\frac{d}{dx}(e^{ax^{4}})
integral from 0 to 1 of cos(2x)	\int\:_{0}^{1}\cos(2x)dx
(\partial)/(\partial y)(5/2 x^2+4xy)	\frac{\partial\:}{\partial\:y}(\frac{5}{2}x^{2}+4xy)
integral of t/(1-t^8)	\int\:\frac{t}{1-t^{8}}dt
(\partial)/(\partial x)((x-y)^{10})	\frac{\partial\:}{\partial\:x}((x-y)^{10})
area x^4,x^2	area\:x^{4},x^{2}
derivative of f(x)=de^{-cx}	derivative\:f(x)=de^{-cx}
integral of (1-x^2)/(2x)	\int\:\frac{1-x^{2}}{2x}dx
f(t)=e^{3t}	f(t)=e^{3t}
tangent of f(x)=8tan(x),(pi/4 ,8)	tangent\:f(x)=8\tan(x),(\frac{π}{4},8)
integral of (e^{sqrt(x+4)})/(sqrt(x+4))	\int\:\frac{e^{\sqrt{x+4}}}{\sqrt{x+4}}dx
2yln(x)ln(y)dx+dy=0	2y\ln(x)\ln(y)dx+dy=0
derivative of (4-2x^2)^3	derivative\:(4-2x^{2})^{3}
x^{'''}+x^{''}=0	x^{\prime\:\prime\:\prime\:}+x^{\prime\:\prime\:}=0
integral of ((x^2+1))/((x^2-2x+2)^2)	\int\:\frac{(x^{2}+1)}{(x^{2}-2x+2)^{2}}dx
integral of sin^2(5x)cos^2(5x)	\int\:\sin^{2}(5x)\cos^{2}(5x)dx
derivative of (t+1)^{2/3}(3t^2-2)^3	derivative\:(t+1)^{\frac{2}{3}}(3t^{2}-2)^{3}
derivative of (e^x/(1+e^x))	\frac{d}{dx}(\frac{e^{x}}{1+e^{x}})
3e^{5x}(dy)/(dx)=-25 x/(y^2)	3e^{5x}\frac{dy}{dx}=-25\frac{x}{y^{2}}
integral of 2tan(θ)	\int\:2\tan(θ)dθ
integral of 4sin^3(xco)s^5x	\int\:4\sin^{3}(xco)s^{5}xdx
derivative of 2e^2	derivative\:2e^{2}
derivative of sec^2(5x*5)	\frac{d}{dx}(\sec^{2}(5x)\cdot\:5)
derivative of (arcsin(2x)/(arccos(2x)))	\frac{d}{dx}(\frac{\arcsin(2x)}{\arccos(2x)})
derivative of x^{1/(1-x})	\frac{d}{dx}(x^{\frac{1}{1-x}})
ty^'-2y=t^3e^{-t}	ty^{\prime\:}-2y=t^{3}e^{-t}
integral from 0 to 8 of sqrt(1+36x)	\int\:_{0}^{8}\sqrt{1+36x}dx
tangent of f(x)=2x^2+4x,\at x=-2	tangent\:f(x)=2x^{2}+4x,\at\:x=-2
derivative of 4(3x^2-2)	\frac{d}{dx}(4(3x^{2}-2))
integral of sin(x)cos(x)+x	\int\:\sin(x)\cos(x)+xdx
limit as x approaches infinity of xsin((4pi)/x)	\lim\:_{x\to\:\infty\:}(x\sin(\frac{4π}{x}))
(\partial)/(\partial z)(x^2)	\frac{\partial\:}{\partial\:z}(x^{2})
laplacetransform sin^2(t)	laplacetransform\:\sin^{2}(t)
tangent of f(x)=2x^3-x^2+9,(2,21)	tangent\:f(x)=2x^{3}-x^{2}+9,(2,21)
integral of 4/(35sin(x)-12cos(x))	\int\:\frac{4}{35\sin(x)-12\cos(x)}dx
y^{''}-2y^'-3y=-9te^{-t}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=-9te^{-t}
integral of fx	\int\:fxdx
integral of (1/5-2/x)	\int\:(\frac{1}{5}-\frac{2}{x})dx
limit as x approaches 8 of x^{7/3}	\lim\:_{x\to\:8}(x^{\frac{7}{3}})
integral of 6cos(2x)	\int\:6\cos(2x)dx
(\partial)/(\partial x)(sqrt(x^2-1))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}-1})
derivative of (x-3x^4tan(x))	\frac{d}{dx}((x-3x^{4})\tan(x))
simplify 3ln(5x)	simplify\:3\ln(5x)
(dy)/(dx)=x*sqrt(1-y^2)	\frac{dy}{dx}=x\cdot\:\sqrt{1-y^{2}}
derivative of (1-x^3/(1+x^3))	\frac{d}{dx}(\frac{1-x^{3}}{1+x^{3}})
integral of n^{-3}	\int\:n^{-3}
derivative of y=(e^{4x^2}+1)/8	derivative\:y=\frac{e^{4x^{2}}+1}{8}
limit as x approaches 1 of (x+7)/(x+3)	\lim\:_{x\to\:1}(\frac{x+7}{x+3})
derivative of x^{2y}	\frac{d}{dx}(x^{2y})
integral of ((3x-4)e^{-x})	\int\:((3x-4)e^{-x})dx
tangent of f(x)= 8/(x^2+4),\at x=3	tangent\:f(x)=\frac{8}{x^{2}+4},\at\:x=3
integral from 0 to 5 of 5x-x^2	\int\:_{0}^{5}5x-x^{2}dx
derivative of y^4-2x	\frac{d}{dx}(y^{4}-2x)
(\partial)/(\partial z)(xy^2)	\frac{\partial\:}{\partial\:z}(xy^{2})
(\partial)/(\partial x)(2xy-28x)	\frac{\partial\:}{\partial\:x}(2xy-28x)
integral of (x^3+6x-2)/(x^4+6x^2)	\int\:\frac{x^{3}+6x-2}{x^{4}+6x^{2}}dx
integral of 5^{-8(x-7)}	\int\:5^{-8(x-7)}dx
integral of a/(a-x)	\int\:\frac{a}{a-x}dx
y^'=((y^2-1))/(xy)	y^{\prime\:}=\frac{(y^{2}-1)}{xy}
derivative of xe^{x^4}	\frac{d}{dx}(xe^{x^{4}})
d/(d{z)}({x}^2{y}{z})	\frac{d}{d{z}}({x}^{2}{y}{z})
integral of x^5*ln(x)	\int\:x^{5}\cdot\:\ln(x)dx
y^{''}+9y=19	y^{\prime\:\prime\:}+9y=19
derivative of f(x)=(x^2)/(8-8x)	derivative\:f(x)=\frac{x^{2}}{8-8x}
derivative of (1/(y^2)-5/(y^4))(y+9y^3)	derivative\:(\frac{1}{y^{2}}-\frac{5}{y^{4}})(y+9y^{3})
(dy)/(dx)= 1/10 y(500-y)	\frac{dy}{dx}=\frac{1}{10}y(500-y)
limit as x approaches infinity of 7x^2+6	\lim\:_{x\to\:\infty\:}(7x^{2}+6)
y^'=tan(x+y)	y^{\prime\:}=\tan(x+y)
integral of sqrt(θ^4+4θ^2)	\int\:\sqrt{θ^{4}+4θ^{2}}dθ

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