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Popular Calculus Problems

integral of-x^2e^{2x}	\int\:-x^{2}e^{2x}dx
derivative of 1/2 tan(xsin(2x))	\frac{d}{dx}(\frac{1}{2}\tan(x)\sin(2x))
integral of 25sec^5(x)	\int\:25\sec^{5}(x)dx
y^{''}+7y^'+10y=14xe^{3x}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=14xe^{3x}
implicit (du)/(dv),sqrt(u)+sqrt(v)=5	implicit\:\frac{du}{dv},\sqrt{u}+\sqrt{v}=5
integral of (1/3 e^{x+3}+3/x-5)	\int\:(\frac{1}{3}e^{x+3}+\frac{3}{x}-5)dx
integral of (x^2-11x-18)/(x(x^2+3x+3))	\int\:\frac{x^{2}-11x-18}{x(x^{2}+3x+3)}dx
(\partial)/(\partial x)(5xy-4x^2y)	\frac{\partial\:}{\partial\:x}(5xy-4x^{2}y)
(\partial)/(\partial x)(x)	\frac{\partial\:}{\partial\:x}(x)
limit as x approaches 0 of sin^4(x)	\lim\:_{x\to\:0}(\sin^{4}(x))
laplacetransform cos(2(t-(5pi)/2))	laplacetransform\:\cos(2(t-\frac{5π}{2}))
slope of (2.3)(1.3)	slope\:(2.3)(1.3)
integral of x/(1+x^4)	\int\:\frac{x}{1+x^{4}}dx
limit as x approaches 0+of 1/(2+e^{1/x)}	\lim\:_{x\to\:0+}(\frac{1}{2+e^{\frac{1}{x}}})
integral from 1 to 9 of (x^2-4x+5)	\int\:_{1}^{9}(x^{2}-4x+5)dx
derivative of x^{log_{e}(x})	\frac{d}{dx}(x^{\log_{e}(x)})
derivative of 1/(3+t)	derivative\:\frac{1}{3+t}
limit as x approaches 3 of (x^2-4)/(x-2)	\lim\:_{x\to\:3}(\frac{x^{2}-4}{x-2})
x+y=(dy)/(dx)	x+y=\frac{dy}{dx}
derivative of xln(x^9)	\frac{d}{dx}(x\ln(x^{9}))
derivative of (1+x^2(x^{3/4}-x^{-3}))	\frac{d}{dx}((1+x^{2})(x^{\frac{3}{4}}-x^{-3}))
limit as x approaches 0-of (e^{2x})/(3x)	\lim\:_{x\to\:0-}(\frac{e^{2x}}{3x})
(\partial)/(\partial x)(A(e^{-x}-e^{-x}x))	\frac{\partial\:}{\partial\:x}(A(e^{-x}-e^{-x}x))
derivative of x^2cot(x)	derivative\:x^{2}\cot(x)
sum from n=0 to infinity of 0.05^n	\sum\:_{n=0}^{\infty\:}0.05^{n}
integral of 2rsqrt(4-r^2)	\int\:2r\sqrt{4-r^{2}}dr
integral of sqrt(x^{11)}	\int\:\sqrt{x^{11}}dx
(\partial)/(\partial y)(x^2+3xy+y-1)	\frac{\partial\:}{\partial\:y}(x^{2}+3xy+y-1)
derivative of (6x-2)^2	derivative\:(6x-2)^{2}
(\partial)/(\partial y)(e^{(x-1)^2})	\frac{\partial\:}{\partial\:y}(e^{(x-1)^{2}})
integral of 8sin(8x)	\int\:8\sin(8x)dx
tangent of y=x^2e^x-2xe^x+2e^x	tangent\:y=x^{2}e^{x}-2xe^{x}+2e^{x}
derivative of f(x)=(24x)/(2x+3)	derivative\:f(x)=\frac{24x}{2x+3}
integral of x/5 sqrt(25+x^2)	\int\:\frac{x}{5}\sqrt{25+x^{2}}dx
integral of \sqrt[3]{t}	\int\:\sqrt[3]{t}dt
derivative of sqrt(3x-1)	derivative\:\sqrt{3x-1}
derivative of x^{1/3}+3	\frac{d}{dx}(x^{\frac{1}{3}}+3)
integral of 6e^3	\int\:6e^{3}dx
integral of e^{4x+e^{4x}}	\int\:e^{4x+e^{4x}}dx
y^'+1/(20x)y=-9.81	y^{\prime\:}+\frac{1}{20x}y=-9.81
derivative of sqrt(5-cos(x))	\frac{d}{dx}(\sqrt{5-\cos(x)})
(\partial)/(\partial x)(2(x-1)^2-3y-5)	\frac{\partial\:}{\partial\:x}(2(x-1)^{2}-3y-5)
y^'=x^3(1-y)	y^{\prime\:}=x^{3}(1-y)
y^'=0.001y(1800-y)	y^{\prime\:}=0.001y(1800-y)
integral of x*e^{-x^2}	\int\:x\cdot\:e^{-x^{2}}dx
(dy)/(dx)=e^{x-y},y(0)=2	\frac{dy}{dx}=e^{x-y},y(0)=2
limit as x approaches 11-of sqrt(x-11)	\lim\:_{x\to\:11-}(\sqrt{x-11})
derivative of e^{x^{x^2}}	derivative\:e^{x^{x^{2}}}
(\partial)/(\partial x)((e^x)/(1-e^x))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{1-e^{x}})
tangent of f(x)=sec(x),\at x= pi/3	tangent\:f(x)=\sec(x),\at\:x=\frac{π}{3}
implicit (d^2y)/(dx^2),3xy+y^2=7	implicit\:\frac{d^{2}y}{dx^{2}},3xy+y^{2}=7
integral of sin(ax+b)	\int\:\sin(ax+b)dx
(\partial)/(\partial x)(6sqrt(x))	\frac{\partial\:}{\partial\:x}(6\sqrt{x})
integral of 8-(160)/(32-x)	\int\:8-\frac{160}{32-x}dx
limit as x approaches 6-of ln(6-x)	\lim\:_{x\to\:6-}(\ln(6-x))
taylor sqrt(-x^2+2x),1	taylor\:\sqrt{-x^{2}+2x},1
(x^2+2xy-y^2)dx+(y^2+2xy-x^2)dy=0	(x^{2}+2xy-y^{2})dx+(y^{2}+2xy-x^{2})dy=0
integral of xsin(x/2)	\int\:x\sin(\frac{x}{2})dx
derivative of sqrt(4-2x)	\frac{d}{dx}(\sqrt{4-2x})
y^{''}+4y^'+16y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+16y=0
derivative of 6ln(x)	derivative\:6\ln(x)
derivative of 27sin(3x)	derivative\:27\sin(3x)
(dy)/(dx)+6/x y=0	\frac{dy}{dx}+\frac{6}{x}y=0
derivative of u^{7/2}	derivative\:u^{\frac{7}{2}}
sum from n=1 to infinity of 2/(n^2+2n)	\sum\:_{n=1}^{\infty\:}\frac{2}{n^{2}+2n}
(\partial)/(\partial x)(rsqrt((g(r,x))/(2h)))	\frac{\partial\:}{\partial\:x}(r\sqrt{\frac{g(r,x)}{2h}})
integral of 1/(sqrt(4x+x^2))	\int\:\frac{1}{\sqrt{4x+x^{2}}}dx
y^2dt+t^2dy=0	y^{2}dt+t^{2}dy=0
d/(dθ)(4cos(3θ))	\frac{d}{dθ}(4\cos(3θ))
integral of 1/(sqrt(1^2+u^2))	\int\:\frac{1}{\sqrt{1^{2}+u^{2}}}du
integral from-ln(4) to 0 of 2sqrt(3)e^t	\int\:_{-\ln(4)}^{0}2\sqrt{3}e^{t}dt
(\partial)/(\partial z)(sin(xyz))	\frac{\partial\:}{\partial\:z}(\sin(xyz))
(\partial)/(\partial x)(e^{13xy})	\frac{\partial\:}{\partial\:x}(e^{13xy})
sum from n=1 to infinity of (cos(n*pi))/(n^{3/8)}	\sum\:_{n=1}^{\infty\:}\frac{\cos(n\cdot\:π)}{n^{\frac{3}{8}}}
limit as x approaches 0 of (sin(pi))/x	\lim\:_{x\to\:0}(\frac{\sin(π)}{x})
derivative of cos(x^2y)	\frac{d}{dx}(\cos(x^{2}y))
y^'=(xy+y^2)/(x^2)	y^{\prime\:}=\frac{xy+y^{2}}{x^{2}}
y^{''}+4y^'+4y=(7+x)e^{-2x}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=(7+x)e^{-2x}
derivative of 1/x+2/(x^2)	\frac{d}{dx}(\frac{1}{x}+\frac{2}{x^{2}})
derivative of (cos(x)^{ln(x)})	\frac{d}{dx}((\cos(x))^{\ln(x)})
derivative of sqrt(2+x)	derivative\:\sqrt{2+x}
derivative of 1/(4y^2)	derivative\:\frac{1}{4y^{2}}
integral from 0 to 1 of-3(x^2+1)e^{-x}	\int\:_{0}^{1}-3(x^{2}+1)e^{-x}dx
integral of 21sin^2(xco)s^2x	\int\:21\sin^{2}(xco)s^{2}x
(\partial)/(\partial x)(1e^1)	\frac{\partial\:}{\partial\:x}(1e^{1})
sum from n=1 to infinity of 1/(n^pi)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{π}}
integral of 4tan^2(θ)	\int\:4\tan^{2}(θ)dθ
(\partial)/(\partial x)(sin(3x^3y-5xy^3))	\frac{\partial\:}{\partial\:x}(\sin(3x^{3}y-5xy^{3}))
tangent of f(x)=7e^xcos(x),(0,7)	tangent\:f(x)=7e^{x}\cos(x),(0,7)
integral of cos^7(7-x)sin(7-x)	\int\:\cos^{7}(7-x)\sin(7-x)dx
integral from 1 to 2 of 15x^22^{x^3}	\int\:_{1}^{2}15x^{2}2^{x^{3}}dx
derivative of (5t+e^t)(3-sqrt(t))	derivative\:(5t+e^{t})(3-\sqrt{t})
(x^2y^3-1/(1+9x^2))((dx)/(dy))+x^3y^2=0	(x^{2}y^{3}-\frac{1}{1+9x^{2}})(\frac{dx}{dy})+x^{3}y^{2}=0
integral of x^2sqrt(1+x^2)	\int\:x^{2}\sqrt{1+x^{2}}dx
(\partial)/(\partial x)(x^2sin(3t))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(3t))
derivative of arcsin(e^{2x})	derivative\:\arcsin(e^{2x})
integral of ln(sin(x))cos^3(x)	\int\:\ln(\sin(x))\cos^{3}(x)dx
t^2(dy)/(dt)+y=0,y(5)=-1,t>0	t^{2}\frac{dy}{dt}+y=0,y(5)=-1,t>0
limit as x approaches-10 of 1/((x+10)^4)	\lim\:_{x\to\:-10}(\frac{1}{(x+10)^{4}})
integral of sqrt(1+8x)	\int\:\sqrt{1+8x}dx

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