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Popular Calculus Problems

integral of (x^2-4)^{1/2}	\int\:(x^{2}-4)^{\frac{1}{2}}dx
integral from 6 to 8 of (10)/((x-6)^3)	\int\:_{6}^{8}\frac{10}{(x-6)^{3}}dx
derivative of f(x)=x^2e^{-7x}	derivative\:f(x)=x^{2}e^{-7x}
integral of x^2*2x	\int\:x^{2}\cdot\:2xdx
integral from 0 to 7 of (7t)/((t-8)^2)	\int\:_{0}^{7}\frac{7t}{(t-8)^{2}}dt
(\partial)/(\partial x)(sin^2(x)cos^2(y))	\frac{\partial\:}{\partial\:x}(\sin^{2}(x)\cos^{2}(y))
simplify-3	simplify\:-3
f(x)=arccos(e^x)	f(x)=\arccos(e^{x})
integral of 2e^x-6x	\int\:2e^{x}-6xdx
6t(dy)/(dt)+y=0	6t\frac{dy}{dt}+y=0
derivative of 1/3 sin^3(x)	\frac{d}{dx}(\frac{1}{3}\sin^{3}(x))
tangent of f(x)=x^2-7,(-4,9)	tangent\:f(x)=x^{2}-7,(-4,9)
derivative of-sin(x^3*3x^2)	\frac{d}{dx}(-\sin(x^{3})\cdot\:3x^{2})
integral of ycos(xy)	\int\:y\cos(xy)dx
integral from 2 to x of (2x-3)/6	\int\:_{2}^{x}\frac{2x-3}{6}dx
derivative of 3sec^2(x)	\frac{d}{dx}(3\sec^{2}(x))
(dy)/(dx)=cos(5x)	\frac{dy}{dx}=\cos(5x)
derivative of tan(u)	derivative\:\tan(u)
derivative of ln((x-1/x))	\frac{d}{dx}(\ln(\frac{x-1}{x}))
derivative of 100(1+Ae^{-t})^{-1}	derivative\:100(1+Ae^{-t})^{-1}
integral of x^5sqrt(7+x^6)	\int\:x^{5}\sqrt{7+x^{6}}dx
integral of t^2cos(2t)	\int\:t^{2}\cos(2t)dt
derivative of (-x^3-x^2+xcos(x))	\frac{d}{dx}((-x^{3}-x^{2}+x)\cos(x))
area f(x)=x*sqrt(1-x^2),[0,1]	area\:f(x)=x\cdot\:\sqrt{1-x^{2}},[0,1]
inverse oflaplace 1/(p(p+1))	inverselaplace\:\frac{1}{p(p+1)}
limit as x approaches-3 of x^2+27	\lim\:_{x\to\:-3}(x^{2}+27)
integral of x^2(x-2/x)	\int\:x^{2}(x-\frac{2}{x})dx
f(x)=arctan((1+x)/(1-x))	f(x)=\arctan(\frac{1+x}{1-x})
(dy)/(dx)=15sin(pi/(20)(x-2))+2	\frac{dy}{dx}=15\sin(\frac{π}{20}(x-2))+2
tangent of y=tan(18x^2),\at x=sqrt(pi)	tangent\:y=\tan(18x^{2}),\at\:x=\sqrt{π}
integral of 2cos(7x-4)	\int\:2\cos(7x-4)dx
y^{''}+9y=csc^2(3t)	y^{\prime\:\prime\:}+9y=\csc^{2}(3t)
y^'=2y-t^2	y^{\prime\:}=2y-t^{2}
integral from 0 to 2 of sin(x^2)	\int\:_{0}^{2}\sin(x^{2})dx
(\partial)/(\partial x)(-xyz^2+16)	\frac{\partial\:}{\partial\:x}(-xyz^{2}+16)
tangent of y=x-x^3(1)	tangent\:y=x-x^{3}(1)
inverse oflaplace 5/(s^2+4)	inverselaplace\:\frac{5}{s^{2}+4}
(\partial)/(\partial x)(-4x^5y^{-5})	\frac{\partial\:}{\partial\:x}(-4x^{5}y^{-5})
(\partial)/(\partial y)(sqrt(1+xy^2))	\frac{\partial\:}{\partial\:y}(\sqrt{1+xy^{2}})
derivative of ln(x^{11})	\frac{d}{dx}(\ln(x^{11}))
(\partial)/(\partial x)(x^2y^3(6-x-y))	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}(6-x-y))
derivative of x^{15}	\frac{d}{dx}(x^{15})
y^'=sin(x)y+e^x	y^{\prime\:}=\sin(x)y+e^{x}
(\partial)/(\partial θ)((cos(θ))/(r(θ)))	\frac{\partial\:}{\partial\:θ}(\frac{\cos(θ)}{r(θ)})
limit as x approaches 2 of 0/((x-2)^2)	\lim\:_{x\to\:2}(\frac{0}{(x-2)^{2}})
integral of 4e^6	\int\:4e^{6}dx
limit as x approaches 3 of x-sqrt(x+1)	\lim\:_{x\to\:3}(x-\sqrt{x+1})
(\partial)/(\partial y)(4x^3y^2-4)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{2}-4)
integral of 1/(x^2sqrt(6x+1))	\int\:\frac{1}{x^{2}\sqrt{6x+1}}dx
inverse oflaplace 1/((s+1)^2)	inverselaplace\:\frac{1}{(s+1)^{2}}
sum from n=0 to infinity of z^{2n+1}	\sum\:_{n=0}^{\infty\:}z^{2n+1}
integral of (7cos(x)+2sin(x))	\int\:(7\cos(x)+2\sin(x))dx
y^{''}+4y=sin(2t)cos(2t)	y^{\prime\:\prime\:}+4y=\sin(2t)\cos(2t)
inverse oflaplace ((e^{-s}))/(s^5)	inverselaplace\:\frac{(e^{-s})}{s^{5}}
implicit x^2+y^2=2	implicit\:x^{2}+y^{2}=2
(\partial)/(\partial x)(3x(4+y)^{-1})	\frac{\partial\:}{\partial\:x}(3x(4+y)^{-1})
integral from 0 to 6 of 1/(sqrt(36+x^2))	\int\:_{0}^{6}\frac{1}{\sqrt{36+x^{2}}}dx
(\partial)/(\partial x)(e^{3y})	\frac{\partial\:}{\partial\:x}(e^{3y})
integral of z/(z^4+4)	\int\:\frac{z}{z^{4}+4}dz
y^{''}+4y^'+3=0	y^{\prime\:\prime\:}+4y^{\prime\:}+3=0
(dy)/(dx)=(x+y-3)^2	\frac{dy}{dx}=(x+y-3)^{2}
taylor cos(x),0	taylor\:\cos(x),0
derivative of x^3+(4x^2/3-2x+5)	\frac{d}{dx}(x^{3}+\frac{4x^{2}}{3}-2x+5)
integral of x^3sqrt(x^2+36)	\int\:x^{3}\sqrt{x^{2}+36}dx
limit as x approaches 0 of ((2x^3))/(2x)	\lim\:_{x\to\:0}(\frac{(2x^{3})}{2x})
integral of e^{2x}*2	\int\:e^{2x}\cdot\:2dx
integral of 6/(x(x-6)^2)	\int\:\frac{6}{x(x-6)^{2}}dx
y^{''}+4y^'+5y=15x+3e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=15x+3e^{-x}
y^{''}+8y^'+7y=-8-x+24x^2+7x^3	y^{\prime\:\prime\:}+8y^{\prime\:}+7y=-8-x+24x^{2}+7x^{3}
integral of x^2*sqrt(1-x^2)	\int\:x^{2}\cdot\:\sqrt{1-x^{2}}dx
y^{''}+121y=cos(6t)	y^{\prime\:\prime\:}+121y=\cos(6t)
integral of (3^{sqrt(x)})/(sqrt(x))	\int\:\frac{3^{\sqrt{x}}}{\sqrt{x}}dx
3y^{''}+8y^'-3y=0	3y^{\prime\:\prime\:}+8y^{\prime\:}-3y=0
integral of (1+cos^2(x))	\int\:(1+\cos^{2}(x))dx
sum from n=1 to infinity of (7^n)/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{7^{n}}{6^{n}}
limit as x approaches infinity of 5e^{-t}i-(5t)/(t+7)j+5arctan(tk)	\lim\:_{x\to\:\infty\:}(5e^{-t}i-\frac{5t}{t+7}j+5\arctan(tk))
y^'=-6y	y^{\prime\:}=-6y
(\partial)/(\partial x)(x^2+y^2+3xy+5x)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+3xy+5x)
x^2y^'+(2-y)=0	x^{2}y^{\prime\:}+(2-y)=0
(\partial)/(\partial y)(2xe^{-y})	\frac{\partial\:}{\partial\:y}(2xe^{-y})
x(dy)/(dx)-y=2x^2	x\frac{dy}{dx}-y=2x^{2}
(\partial)/(\partial x)(3^x)	\frac{\partial\:}{\partial\:x}(3^{x})
(\partial)/(\partial x)(7xy^3+5)	\frac{\partial\:}{\partial\:x}(7xy^{3}+5)
t^2y^'+2ty-y^3=0	t^{2}y^{\prime\:}+2ty-y^{3}=0
inverse oflaplace 1/((s^2+1)(s^2+3))	inverselaplace\:\frac{1}{(s^{2}+1)(s^{2}+3)}
derivative of ln\|t\|	derivative\:\ln\left\|t\right\|
integral of (4x^3)/(x^2+x)	\int\:\frac{4x^{3}}{x^{2}+x}dx
derivative of ((x+1))/(x-1)	derivative\:\frac{(x+1)}{x-1}
tangent of y=sin(2x)ln(x^2),(1,0)	tangent\:y=\sin(2x)\ln(x^{2}),(1,0)
integral of v/(1+v^2)	\int\:\frac{v}{1+v^{2}}dv
integral of sinh(x)cosh(x)	\int\:\sinh(x)\cosh(x)dx
derivative of y=5e^x+4/(\sqrt[3]{x)}	derivative\:y=5e^{x}+\frac{4}{\sqrt[3]{x}}
taylor sqrt(1-x),0	taylor\:\sqrt{1-x},0
y^{'''}+3y^{''}-4y=0	y^{\prime\:\prime\:\prime\:}+3y^{\prime\:\prime\:}-4y=0
y^{''}+3y^'+2y=cos(2x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\cos(2x)
y^'+y-e^x=0	y^{\prime\:}+y-e^{x}=0
area y=x,y=x^3,[-1,2]	area\:y=x,y=x^{3},[-1,2]
integral of-e^{2t}	\int\:-e^{2t}dt
((3y^2-t^2))/(y^5)(dy)/(dt)+t/(2y^4)=0	\frac{(3y^{2}-t^{2})}{y^{5}}\frac{dy}{dt}+\frac{t}{2y^{4}}=0
(\partial)/(\partial y)(cos(x^3y^3))	\frac{\partial\:}{\partial\:y}(\cos(x^{3}y^{3}))

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