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Popular Calculus Problems

integral of 3sin(x)sqrt(1+cos(x))	\int\:3\sin(x)\sqrt{1+\cos(x)}dx
derivative of 3+2x	\frac{d}{dx}(3+2x)
tangent of f(x)= x/(x-2),\at x=1	tangent\:f(x)=\frac{x}{x-2},\at\:x=1
integral of (5x^3+4x)/(x-1)	\int\:\frac{5x^{3}+4x}{x-1}dx
integral of (sqrt(x-4))/x	\int\:\frac{\sqrt{x-4}}{x}dx
y^'=(7x^6e^{y/x}+x^4y^2)/(x^5y)	y^{\prime\:}=\frac{7x^{6}e^{\frac{y}{x}}+x^{4}y^{2}}{x^{5}y}
slope of (-8,-3),(-3,4)	slope\:(-8,-3),(-3,4)
tangent of f(x)= 5/(sqrt(x)),\at x=1	tangent\:f(x)=\frac{5}{\sqrt{x}},\at\:x=1
inverse oflaplace 1/(2s+3)	inverselaplace\:\frac{1}{2s+3}
(\partial)/(\partial y)(xye^{2y})	\frac{\partial\:}{\partial\:y}(xye^{2y})
limit as x approaches 1 of arcsec(x)	\lim\:_{x\to\:1}(\arcsec(x))
integral of cos(3t)+sin(4t)	\int\:\cos(3t)+\sin(4t)dt
derivative of sqrt(x^3)+1/(sqrt(x))	\frac{d}{dx}(\sqrt{x^{3}}+\frac{1}{\sqrt{x}})
integral from 0 to infinity of 70(e^x)/(e^{2x)+3}	\int\:_{0}^{\infty\:}70\frac{e^{x}}{e^{2x}+3}dx
derivative of 7e^xcos(x)	derivative\:7e^{x}\cos(x)
(8+x)y^'=3y	(8+x)y^{\prime\:}=3y
integral of 5\sqrt[3]{x^2}	\int\:5\sqrt[3]{x^{2}}dx
integral of 1/(5x^5)	\int\:\frac{1}{5x^{5}}dx
derivative of f(x)= 1/(3x^2+4x)	derivative\:f(x)=\frac{1}{3x^{2}+4x}
(\partial}{\partial z}(\frac{(3x+y))/z)	\frac{\partial\:}{\partial\:z}(\frac{(3x+y)}{z})
(dy)/(dt)=-y+5	\frac{dy}{dt}=-y+5
y^{''}+9y^'=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+9y^{\prime\:}=0,y(0)=1,y^{\prime\:}(0)=1
integral of (sqrt(y^2-9))/y	\int\:\frac{\sqrt{y^{2}-9}}{y}dy
area 9x-x^2,2x,0,7	area\:9x-x^{2},2x,0,7
derivative of sqrt(4-4x^2)	\frac{d}{dx}(\sqrt{4-4x^{2}})
(d^2y)/(dx^2)+((dy)/(dx))^2=0	\frac{d^{2}y}{dx^{2}}+(\frac{dy}{dx})^{2}=0
derivative of h(x)=x^{6/5}	derivative\:h(x)=x^{\frac{6}{5}}
(d^2)/(dx^2)(4x^3-3x^4)	\frac{d^{2}}{dx^{2}}(4x^{3}-3x^{4})
limit as x approaches 0 of (ln(x))/(1/x)	\lim\:_{x\to\:0}(\frac{\ln(x)}{\frac{1}{x}})
integral from 0 to 8 of sqrt(64-x^2)	\int\:_{0}^{8}\sqrt{64-x^{2}}dx
integral from 0 to 1 of te^{-1}	\int\:_{0}^{1}te^{-1}dt
(x^2+1)((dy)/(dx))+8x(y-1)=0,y(0)=5	(x^{2}+1)(\frac{dy}{dx})+8x(y-1)=0,y(0)=5
integral of 3x^5e^x	\int\:3x^{5}e^{x}dx
6x+(dy)/(dx)=0	6x+\frac{dy}{dx}=0
(\partial)/(\partial x)(x(x^2+y^2+z^2)^m)	\frac{\partial\:}{\partial\:x}(x(x^{2}+y^{2}+z^{2})^{m})
derivative of 1/({f(x)})	\frac{d}{dx}(\frac{1}{{f}(x)})
integral from 1 to-1 of (x-1)(3x+2)	\int\:_{1}^{-1}(x-1)(3x+2)dx
integral of x\sqrt[4]{5x+7}	\int\:x\sqrt[4]{5x+7}dx
derivative of 2/(sin(x+cos(x)))	\frac{d}{dx}(\frac{2}{\sin(x)+\cos(x)})
t(dy)/(dt)=t^3+25t^3y	t\frac{dy}{dt}=t^{3}+25t^{3}y
integral of (ysin(xy))	\int\:(y\sin(xy))dx
(\partial)/(\partial x)(y^2-4x^2+7y+5x+13)	\frac{\partial\:}{\partial\:x}(y^{2}-4x^{2}+7y+5x+13)
y^'+5(cos(5x))y=-8cos(5x)	y^{\prime\:}+5(\cos(5x))y=-8\cos(5x)
area y^2=4x,y^2=8x-4,x	area\:y^{2}=4x,y^{2}=8x-4,x
limit as x approaches 42 of (x^2)/6-7/x	\lim\:_{x\to\:42}(\frac{x^{2}}{6}-\frac{7}{x})
inverse oflaplace (1+10s)/(s^2+10.1s+1)	inverselaplace\:\frac{1+10s}{s^{2}+10.1s+1}
integral of (2x)/(\sqrt[4]{1-x^2)}	\int\:\frac{2x}{\sqrt[4]{1-x^{2}}}dx
(\partial)/(\partial x)((xy-5)^2)	\frac{\partial\:}{\partial\:x}((xy-5)^{2})
limit as x approaches 0 of ((e)^x)/x	\lim\:_{x\to\:0}(\frac{(e)^{x}}{x})
derivative of (3x-4(x^3+5))	\frac{d}{dx}((3x-4)(x^{3}+5))
integral of-sec^3(x)	\int\:-\sec^{3}(x)dx
derivative of f(x)^2	derivative\:f(x)^{2}
derivative of (2x+1^{1/2})	\frac{d}{dx}((2x+1)^{\frac{1}{2}})
derivative of 2/((x+2^2))	\frac{d}{dx}(\frac{2}{(x+2)^{2}})
sum from n=1 to infinity of 0.9^nn^3	\sum\:_{n=1}^{\infty\:}0.9^{n}n^{3}
integral from 10 to 13 of 2x	\int\:_{10}^{13}2xdx
derivative of y=x^2e^{-x}	derivative\:y=x^{2}e^{-x}
(dy)/(dx)+y/(x+2)=5(x-2)y^{1/2}	\frac{dy}{dx}+\frac{y}{x+2}=5(x-2)y^{\frac{1}{2}}
derivative of y=4x-3x^2	derivative\:y=4x-3x^{2}
integral of 1/(x(x^3-1))	\int\:\frac{1}{x(x^{3}-1)}dx
sum from n=1 to infinity of 2/(pi^n)	\sum\:_{n=1}^{\infty\:}\frac{2}{π^{n}}
integral of (x^5)/5	\int\:\frac{x^{5}}{5}dx
limit as x approaches infinity of (4^x)/(3^{x-1)}	\lim\:_{x\to\:\infty\:}(\frac{4^{x}}{3^{x-1}})
integral of \sqrt[3]{8x}	\int\:\sqrt[3]{8x}dx
(\partial)/(\partial x)(y/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{y^{2}+x^{2}})
derivative of (2x^3-x^2+5x/(x^2-25))	\frac{d}{dx}(\frac{2x^{3}-x^{2}+5x}{x^{2}-25})
integral of (6-y)/(y-1)	\int\:\frac{6-y}{y-1}dy
integral from 2 to 8 of (10-x)	\int\:_{2}^{8}(10-x)dx
derivative of f(x)=(2x^7-3x^5+2)^{22}	derivative\:f(x)=(2x^{7}-3x^{5}+2)^{22}
inverse oflaplace (s+3)/(s^2+3s+2)	inverselaplace\:\frac{s+3}{s^{2}+3s+2}
(\partial)/(\partial x)(xsqrt(y-z))	\frac{\partial\:}{\partial\:x}(x\sqrt{y-z})
derivative of f(x)=(x^2+6)/(9x-2)	derivative\:f(x)=\frac{x^{2}+6}{9x-2}
(\partial)/(\partial x)(t^2)	\frac{\partial\:}{\partial\:x}(t^{2})
integral of (x^2)/(sqrt(4-x^2))	\int\:\frac{x^{2}}{\sqrt{4-x^{2}}}dx
integral of (x^2+x^3)	\int\:(x^{2}+x^{3})dx
(dx)/(dt)=2x-x^2	\frac{dx}{dt}=2x-x^{2}
(\partial)/(\partial x)(3x-(3/4 x+1/4 y)^2)	\frac{\partial\:}{\partial\:x}(3x-(\frac{3}{4}x+\frac{1}{4}y)^{2})
x(dy)/(dx)+(1+x)y=e^{-x}sin(2x)	x\frac{dy}{dx}+(1+x)y=e^{-x}\sin(2x)
(dy)/(dx)=-1+(2x+y)^2	\frac{dy}{dx}=-1+(2x+y)^{2}
(\partial)/(\partial x)(4xe^{sqrt(xy)})	\frac{\partial\:}{\partial\:x}(4xe^{\sqrt{xy}})
derivative of e^{cos(x)}+cos(e^x)	derivative\:e^{\cos(x)}+\cos(e^{x})
limit as x approaches 1 of sqrt(1-x^2)	\lim\:_{x\to\:1}(\sqrt{1-x^{2}})
derivative of (x^3+5/x)	\frac{d}{dx}(\frac{x^{3}+5}{x})
derivative of ,xe^y+y^2x-x^3,\at (1,0)	\frac{d}{dx}(,xe^{y}+y^{2}x-x^{3},\at\:(1,0))
sum from n=0 to infinity of 1/(1+n^2)	\sum\:_{n=0}^{\infty\:}\frac{1}{1+n^{2}}
integral of x^2arcsin(x)	\int\:x^{2}\arcsin(x)dx
inverse oflaplace {(s+1)/(s^2-4s)}	inverselaplace\:\left\{\frac{s+1}{s^{2}-4s}\right\}
integral of (x+1)sqrt(2x+x^2)	\int\:(x+1)\sqrt{2x+x^{2}}dx
derivative of-2/(5sqrt(x))	\frac{d}{dx}(-\frac{2}{5\sqrt{x}})
derivative of (x^4)/4-(3x^2)/4+x-2	derivative\:\frac{x^{4}}{4}-\frac{3x^{2}}{4}+x-2
derivative of (x+2/(ln(x)))	\frac{d}{dx}(\frac{x+2}{\ln(x)})
tangent of f(x)=x^2-7x+7,(6,1)	tangent\:f(x)=x^{2}-7x+7,(6,1)
y^{''}+3y^'+2y=20e^{3t}	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=20e^{3t}
inverse oflaplace 3/(s(s^3+2s^2+2s+1))	inverselaplace\:\frac{3}{s(s^{3}+2s^{2}+2s+1)}
(\partial}{\partial y}(e^{y/x}-\frac{e^{y/x}y)/x)	\frac{\partial\:}{\partial\:y}(e^{\frac{y}{x}}-\frac{e^{\frac{y}{x}}y}{x})
laplacetransform sqrt(t)+3t	laplacetransform\:\sqrt{t}+3t
sum from n=0 to infinity of 2(2/3)^{3n}	\sum\:_{n=0}^{\infty\:}2(\frac{2}{3})^{3n}
integral of x/(sqrt(x+1)-(x+1))	\int\:\frac{x}{\sqrt{x+1}-(x+1)}dx
(\partial)/(\partial y)(x^2e^{yz^2})	\frac{\partial\:}{\partial\:y}(x^{2}e^{yz^{2}})
integral from 0 to 1 of xsqrt(1-x)	\int\:_{0}^{1}x\sqrt{1-x}dx

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