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Popular Calculus Problems

integral from 3 to 9 of 1/(xln(x))	\int\:_{3}^{9}\frac{1}{x\ln(x)}dx
tangent of y=sqrt(2x+1),\at x= 1/2	tangent\:y=\sqrt{2x+1},\at\:x=\frac{1}{2}
integral of (x^2+1)/(2x)	\int\:\frac{x^{2}+1}{2x}dx
integral of x/(x^3+x)	\int\:\frac{x}{x^{3}+x}dx
sum from n=0 to infinity of 2^{-n/2}	\sum\:_{n=0}^{\infty\:}2^{-\frac{n}{2}}
derivative of y=ln(5x^2+3y^2)	derivative\:y=\ln(5x^{2}+3y^{2})
limit as x approaches 4+of (2x)/(x-4)	\lim\:_{x\to\:4+}(\frac{2x}{x-4})
integral of (tan^3(7/z))/(z^2)	\int\:\frac{\tan^{3}(\frac{7}{z})}{z^{2}}dz
(\partial)/(\partial z)(xe^{2yz})	\frac{\partial\:}{\partial\:z}(xe^{2yz})
(\partial)/(\partial x)(2/((x-3t)^2+1))	\frac{\partial\:}{\partial\:x}(\frac{2}{(x-3t)^{2}+1})
derivative of (5x+4)/(5x-4)	derivative\:\frac{5x+4}{5x-4}
integral of (x-4)	\int\:(x-4)dx
limit as x approaches 1-of 1/((x-1))	\lim\:_{x\to\:1-}(\frac{1}{(x-1)})
(\partial)/(\partial y)(4x^3+4xy-1)	\frac{\partial\:}{\partial\:y}(4x^{3}+4xy-1)
tangent of ((x^2-1))/((x^2+x+1))	tangent\:\frac{(x^{2}-1)}{(x^{2}+x+1)}
d/(dθ)(5/(2cos(θ)+7sin(θ)))	\frac{d}{dθ}(\frac{5}{2\cos(θ)+7\sin(θ)})
(dy}{dx}=\frac{(x+1))/y	\frac{dy}{dx}=\frac{(x+1)}{y}
(\partial)/(\partial y)(xye^{-5y})	\frac{\partial\:}{\partial\:y}(xye^{-5y})
derivative of (16/(x^3))	\frac{d}{dx}(\frac{16}{x^{3}})
5y^'+y=-3	5y^{\prime\:}+y=-3
tangent of f(x)=3x^4-8x^3+2	tangent\:f(x)=3x^{4}-8x^{3}+2
derivative of 5e^{-2x}sin(3x)	\frac{d}{dx}(5e^{-2x}\sin(3x))
maclaurin (1+x)^{-5/3}	maclaurin\:(1+x)^{-\frac{5}{3}}
(\partial)/(\partial x)(ln(xy))	\frac{\partial\:}{\partial\:x}(\ln(xy))
derivative of x^3e^{-x}	\frac{d}{dx}(x^{3}e^{-x})
limit as x approaches 9 of x+7	\lim\:_{x\to\:9}(x+7)
d/(dt)(10^{2sqrt(t)})	\frac{d}{dt}(10^{2\sqrt{t}})
derivative of 3^t(5t^4+7t+{y}(t,x(t,x)^4))	\frac{d}{dx}(3^{t}(5t^{4}+7t+{y}(t,x)(t,x)^{4}))
derivative of y=x^{2/5}(x+3)	derivative\:y=x^{\frac{2}{5}}(x+3)
integral of (sin(7x))/(1+cos^2(7x))	\int\:\frac{\sin(7x)}{1+\cos^{2}(7x)}dx
derivative of (x^3-4/(x-1))	\frac{d}{dx}(\frac{x^{3}-4}{x-1})
(dy)/(dx)=(ln(x))/(xy),y(1)=2	\frac{dy}{dx}=\frac{\ln(x)}{xy},y(1)=2
derivative of y=((t^3+t))/((t^4-2))	derivative\:y=\frac{(t^{3}+t)}{(t^{4}-2)}
integral of 1/((y^2-1))	\int\:\frac{1}{(y^{2}-1)}dy
derivative of cos^3(x)+sin^4(x)	derivative\:\cos^{3}(x)+\sin^{4}(x)
integral of (3x-2)/(x+1)	\int\:\frac{3x-2}{x+1}dx
(\partial)/(\partial x)((2x^2)/((2x+7y)^2))	\frac{\partial\:}{\partial\:x}(\frac{2x^{2}}{(2x+7y)^{2}})
limit as x approaches-3 of \|-x-1\|	\lim\:_{x\to\:-3}(\left\|-x-1\right\|)
integral of 1/((x-3)(x-1))	\int\:\frac{1}{(x-3)(x-1)}dx
derivative of 6/5-6/5 e^{-20t}	derivative\:\frac{6}{5}-\frac{6}{5}e^{-20t}
f(x)=(2-xe^x)/(x+e^x)	f(x)=\frac{2-xe^{x}}{x+e^{x}}
longdivision (x^2+1)/(x^2-4)	longdivision\:\frac{x^{2}+1}{x^{2}-4}
integral of (x+6)/(x^2+9)	\int\:\frac{x+6}{x^{2}+9}dx
integral from-3 to-2 of 5(2x+4)^{1/3}	\int\:_{-3}^{-2}5(2x+4)^{\frac{1}{3}}dx
(dy)/(dx)=4-y	\frac{dy}{dx}=4-y
integral of (x^3)/9	\int\:\frac{x^{3}}{9}dx
derivative of f(x)=(7x)/(3+x^2)	derivative\:f(x)=\frac{7x}{3+x^{2}}
y^'+y/x-sqrt(y)=0,y(1)=0	y^{\prime\:}+\frac{y}{x}-\sqrt{y}=0,y(1)=0
integral of (sec^2(x)-sin(x))	\int\:(\sec^{2}(x)-\sin(x))dx
taylor sqrt(x),x=4	taylor\:\sqrt{x},x=4
integral of (3x+1)/((x-2)(x+3))	\int\:\frac{3x+1}{(x-2)(x+3)}dx
integral of x-ln(x)	\int\:x-\ln(x)dx
integral from 0 to pi/8 of cos^2(2x)	\int\:_{0}^{\frac{π}{8}}\cos^{2}(2x)dx
taylor x^5cos(x^2)	taylor\:x^{5}\cos(x^{2})
derivative of (3x^{5x})	\frac{d}{dx}((3x)^{5x})
integral of sqrt(ax+b)	\int\:\sqrt{ax+b}dx
derivative of in(xinx)	\frac{d}{dx}(in(xinx))
derivative of 11-x+4ln(2x-1)	\frac{d}{dx}(11-x+4\ln(2x-1))
limit as x approaches 0 of (\|x-4\|)/(x-4)	\lim\:_{x\to\:0}(\frac{\left\|x-4\right\|}{x-4})
derivative of x+y+1	\frac{d}{dx}(x+y+1)
derivative of f(x)=2e^{2e^x+x}	derivative\:f(x)=2e^{2e^{x}+x}
derivative of 3/(y^4)	derivative\:\frac{3}{y^{4}}
y^{''}+2y^'+y=2^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=2^{-t}
derivative of (cos(x))/x	derivative\:\frac{\cos(x)}{x}
integral of ((e^x-1)/(e^x+1))	\int\:(\frac{e^{x}-1}{e^{x}+1})dx
derivative of sqrt(25+(12-x^2)+x)	\frac{d}{dx}(\sqrt{25+(12-x)^{2}}+x)
integral of e^{iax}	\int\:e^{iax}dx
integral of e^{e^t}	\int\:e^{e^{t}}dt
(\partial)/(\partial y)(x^2y+3xy+y^2)	\frac{\partial\:}{\partial\:y}(x^{2}y+3xy+y^{2})
(1/(1-x^2))^'	(\frac{1}{1-x^{2}})^{\prime\:}
integral of x/(\sqrt[3]{x+8)}	\int\:\frac{x}{\sqrt[3]{x+8}}dx
laplacetransform e^{3t}cos(6t)	laplacetransform\:e^{3t}\cos(6t)
integral of 3a^7x^6	\int\:3a^{7}x^{6}dx
limit as x approaches 1 of e^{(x^2-x)}	\lim\:_{x\to\:1}(e^{(x^{2}-x)})
derivative of x^3-3x^2+2	\frac{d}{dx}(x^{3}-3x^{2}+2)
derivative of 1+e^{-x}	derivative\:1+e^{-x}
integral of (x+1)e^{-x}	\int\:(x+1)e^{-x}dx
integral of xe^{0.2x}	\int\:xe^{0.2x}dx
derivative of f(x)=x^3+3x	derivative\:f(x)=x^{3}+3x
taylor x^{5/7}	taylor\:x^{\frac{5}{7}}
derivative of f(x)=(x+9)/(x-9)	derivative\:f(x)=\frac{x+9}{x-9}
t^2y^{''}-5ty^'+9y=0	t^{2}y^{\prime\:\prime\:}-5ty^{\prime\:}+9y=0
derivative of xcos(3x)	derivative\:x\cos(3x)
y^'=xe^y,y(0)=0	y^{\prime\:}=xe^{y},y(0)=0
derivative of arctan^2(1/x)	\frac{d}{dx}(\arctan^{2}(\frac{1}{x}))
derivative of 2sin(x-3cos(x))	\frac{d}{dx}(2\sin(x)-3\cos(x))
integral of 20arctan(sqrt(x))	\int\:20\arctan(\sqrt{x})dx
derivative of 5e^{-x}-6e^x	\frac{d}{dx}(5e^{-x}-6e^{x})
derivative of y=sqrt(4+3x)	derivative\:y=\sqrt{4+3x}
derivative of (ln(x)^{sqrt(ln(x))})	\frac{d}{dx}((\ln(x))^{\sqrt{\ln(x)}})
integral from 0 to 1 of x^3e^x	\int\:_{0}^{1}x^{3}e^{x}dx
limit as x approaches 25 of 2x+2sqrt(x)	\lim\:_{x\to\:25}(2x+2\sqrt{x})
integral of-9cos(x)	\int\:-9\cos(x)dx
limit as x approaches 3 of (x-1)/(x^2-2)	\lim\:_{x\to\:3}(\frac{x-1}{x^{2}-2})
derivative of x^6+x	\frac{d}{dx}(x^{6}+x)
xy^2dx=dy-xdx	xy^{2}dx=dy-xdx
limit as x approaches 0 of sin((4pi)/x)	\lim\:_{x\to\:0}(\sin(\frac{4π}{x}))
derivative of f(x)=\sqrt[5]{x^2}	derivative\:f(x)=\sqrt[5]{x^{2}}
limit as x approaches 0 of (tan(9x))/x	\lim\:_{x\to\:0}(\frac{\tan(9x)}{x})
integral of sqrt(144-4x^2)	\int\:\sqrt{144-4x^{2}}dx

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