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Popular Calculus Problems

limit as x approaches+0 of x^8-1/x	\lim\:_{x\to\:+0}(x^{8}-\frac{1}{x})
limit as x approaches 1-of (x-1)/(\|x-1\|)	\lim\:_{x\to\:1-}(\frac{x-1}{\left\|x-1\right\|})
integral of-xsin(y)+2y	\int\:-x\sin(y)+2ydy
integral of x(x+9)^{10}	\int\:x(x+9)^{10}dx
integral of (sec(x))/(tan(x))	\int\:\frac{\sec(x)}{\tan(x)}dx
y^{23}dy=xdx	y^{23}dy=xdx
limit as x approaches 0 of 3/(x(x-1))	\lim\:_{x\to\:0}(\frac{3}{x(x-1)})
integral of (x^3)/(sqrt(x^2+81))	\int\:\frac{x^{3}}{\sqrt{x^{2}+81}}dx
derivative of f(x)=sqrt((2x^2-x)/(x+5))	derivative\:f(x)=\sqrt{\frac{2x^{2}-x}{x+5}}
integral of 3arctan(x)	\int\:3\arctan(x)dx
derivative of 5x^2+1/(x^2)	derivative\:5x^{2}+\frac{1}{x^{2}}
derivative of (x+1)/(x^3+x-3)	derivative\:\frac{x+1}{x^{3}+x-3}
limit as x approaches 1 of xln(x)	\lim\:_{x\to\:1}(x\ln(x))
integral of 1/(x+2)	\int\:\frac{1}{x+2}dx
derivative of sqrt(2-5x)	\frac{d}{dx}(\sqrt{2-5x})
taylor ln((x/2)^2+4^2)	taylor\:\ln((\frac{x}{2})^{2}+4^{2})
integral from-2 to 2 of 1/(1+x^2)	\int\:_{-2}^{2}\frac{1}{1+x^{2}}dx
derivative of f(x)=(2x)/(2e^{9x)}	derivative\:f(x)=\frac{2x}{2e^{9x}}
derivative of ln(3x-5)	\frac{d}{dx}(\ln(3x-5))
derivative of y=((x-2)(x^2+2x+4))/(x^3)	derivative\:y=\frac{(x-2)(x^{2}+2x+4)}{x^{3}}
derivative of sqrt(x^2+y^2)	derivative\:\sqrt{x^{2}+y^{2}}
integral from 0 to 1 of 2pi(y)(y-y^3)	\int\:_{0}^{1}2π(y)(y-y^{3})dy
integral of y^6(cos(3y))	\int\:y^{6}(\cos(3y))dy
integral of (1/x)^2	\int\:(\frac{1}{x})^{2}dx
inverse oflaplace 1/((s^4)(s-5))	inverselaplace\:\frac{1}{(s^{4})(s-5)}
integral of e^{4x+2}	\int\:e^{4x+2}dx
integral of ((2x+7))/(x+3)	\int\:\frac{(2x+7)}{x+3}dx
integral of (x+4)sin(npix)	\int\:(x+4)\sin(nπx)dx
sum from n=1 to infinity of 8(1/4)^n	\sum\:_{n=1}^{\infty\:}8(\frac{1}{4})^{n}
integral of ce^{cx}	\int\:ce^{cx}dx
(\partial)/(\partial x)(rcos(x)sin(y))	\frac{\partial\:}{\partial\:x}(r\cos(x)\sin(y))
(dy)/(dt)=ky(1-y/(4600))	\frac{dy}{dt}=ky(1-\frac{y}{4600})
area f(x)=8sin(x),g(x)=8cos(2x)	area\:f(x)=8\sin(x),g(x)=8\cos(2x)
derivative of f(x)= 1/6 (2x+1)^3	derivative\:f(x)=\frac{1}{6}(2x+1)^{3}
integral of ((x^5-x^3+6x))/(x^4)	\int\:\frac{(x^{5}-x^{3}+6x)}{x^{4}}dx
area x^3-11x^2+30x,-x^3+11x^2-30x	area\:x^{3}-11x^{2}+30x,-x^{3}+11x^{2}-30x
derivative of f(x)=(x-2)^3(x-1)	derivative\:f(x)=(x-2)^{3}(x-1)
y^{''}+36y=-24sin(6t)	y^{\prime\:\prime\:}+36y=-24\sin(6t)
(sqrt(x)e^x)^'	(\sqrt{x}e^{x})^{\prime\:}
(e^x+y)dx+(e^y+x)dy=0	(e^{x}+y)dx+(e^{y}+x)dy=0
(\partial)/(\partial x)(2xsin(y))	\frac{\partial\:}{\partial\:x}(2x\sin(y))
derivative of (x-1^{1/2})	\frac{d}{dx}((x-1)^{\frac{1}{2}})
derivative of sin(3x^2+2x^3)	\frac{d}{dx}(\sin(3x^{2})+2x^{3})
(\partial)/(\partial x)(ye^{y/x})	\frac{\partial\:}{\partial\:x}(ye^{\frac{y}{x}})
integral of (sin(3x))	\int\:(\sin(3x))dx
(\partial)/(\partial x)(6cos^4(3x+2))	\frac{\partial\:}{\partial\:x}(6\cos^{4}(3x+2))
derivative of sqrt(e^{2x)+e^{-2x}}	\frac{d}{dx}(\sqrt{e^{2x}+e^{-2x}})
(x-3)^'	(x-3)^{\prime\:}
derivative of xe^{(x^2/2})	\frac{d}{dx}(xe^{\frac{x^{2}}{2}})
integral of (3+4x)/(1+x^2)	\int\:\frac{3+4x}{1+x^{2}}dx
integral from 0 to pi/4 of x^2cos(2x)	\int\:_{0}^{\frac{π}{4}}x^{2}\cos(2x)dx
f(x)=cos(8x)	f(x)=\cos(8x)
y^{''}+5y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+5y=0,y(0)=1,y^{\prime\:}(0)=1
(\partial)/(\partial x)(cos(2y-x))	\frac{\partial\:}{\partial\:x}(\cos(2y-x))
derivative of log_{10}(\|1-2x^2\|)	\frac{d}{dx}(\log_{10}(\left\|1-2x^{2}\right\|))
(1+ln(x)+y/x)dx=(6-ln(x))dy	(1+\ln(x)+\frac{y}{x})dx=(6-\ln(x))dy
(xdy)/(dx)-(2dy)/(dx)-(x-2)sin(x)+y=0	\frac{xdy}{dx}-\frac{2dy}{dx}-(x-2)\sin(x)+y=0
(\partial)/(\partial x)(4xe^x)	\frac{\partial\:}{\partial\:x}(4xe^{x})
integral from 0 to infinity of xe^{-ax}	\int\:_{0}^{\infty\:}xe^{-ax}dx
derivative of (e^{2x}-1/(1-e^{-2x)})	\frac{d}{dx}(\frac{e^{2x}-1}{1-e^{-2x}})
derivative of (x^2+17(x^3-3x+1))	\frac{d}{dx}((x^{2}+17)(x^{3}-3x+1))
y^{''}+9y=9x^2+9x+11	y^{\prime\:\prime\:}+9y=9x^{2}+9x+11
x(dy)/(dx)+yln(x)-y=yln(y)	x\frac{dy}{dx}+y\ln(x)-y=y\ln(y)
(\partial)/(\partial y)(1/(x^2yz))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{2}yz})
(dy)/(dt)-5/t y=t^5	\frac{dy}{dt}-\frac{5}{t}y=t^{5}
derivative of (-1x+sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{-1x+\sqrt{1+x}}{x^{2}-1})
derivative of 1-5cos(x)	\frac{d}{dx}(1-5\cos(x))
limit as x approaches+3 of 6x^2	\lim\:_{x\to\:+3}(6x^{2})
derivative of cx^2e^{(-mx^2/(2kt)})	\frac{d}{dx}(c\cdot\:x^{2}\cdot\:e^{\frac{-mx^{2}}{2kt}})
integral of ((tan(x))/(cos(x)))	\int\:(\frac{\tan(x)}{\cos(x)})dx
integral of sin^3(x)cos^{12}(x)	\int\:\sin^{3}(x)\cos^{12}(x)dx
integral from 0 to infinity of 1/(x^4-1)	\int\:_{0}^{\infty\:}\frac{1}{x^{4}-1}dx
integral from 7 to 8 of x/(x^2+6x+13)	\int\:_{7}^{8}\frac{x}{x^{2}+6x+13}dx
(\partial)/(\partial y)(ycos(6x))	\frac{\partial\:}{\partial\:y}(y\cos(6x))
tangent of f(x)=sqrt(x)\at (25.5)	tangent\:f(x)=\sqrt{x}\at\:(25.5)
integral from 1 to 3 of (u-2)^4	\int\:_{1}^{3}(u-2)^{4}du
integral of e^{8x}cos(7x)	\int\:e^{8x}\cos(7x)dx
integral of x^{12}	\int\:x^{12}dx
limit as x approaches 2-of \|x-2\|	\lim\:_{x\to\:2-}(\left\|x-2\right\|)
(\partial)/(\partial x)(e^{-x}sin(x+y))	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(x+y))
derivative of 0.5x^2	\frac{d}{dx}(0.5x^{2})
(\partial)/(\partial y)(y/(x^2))	\frac{\partial\:}{\partial\:y}(\frac{y}{x^{2}})
slope of (5.5)(0.4)	slope\:(5.5)(0.4)
inverse oflaplace 2/((s^2+4))	inverselaplace\:\frac{2}{(s^{2}+4)}
area y=x,y=2xsqrt(1-x^2)	area\:y=x,y=2x\sqrt{1-x^{2}}
derivative of e^xsin(x^2)	\frac{d}{dx}(e^{x}\sin(x^{2}))
derivative of 2x+sin(2x)	\frac{d}{dx}(2x+\sin(2x))
(\partial)/(\partial y)(xe^{7xy})	\frac{\partial\:}{\partial\:y}(xe^{7xy})
integral of e^{(x-1)}	\int\:e^{(x-1)}dx
(dy)/(dx)=ye^{-x^2}	\frac{dy}{dx}=ye^{-x^{2}}
(\partial)/(\partial x)(e^{x+y+9})	\frac{\partial\:}{\partial\:x}(e^{x+y+9})
integral of e^{r/2}	\int\:e^{\frac{r}{2}}dr
integral of-10	\int\:-10dx
(\partial)/(\partial x)(x^{-2}y^{-3})	\frac{\partial\:}{\partial\:x}(x^{-2}y^{-3})
integral of (7^x-sec^2(x))	\int\:(7^{x}-\sec^{2}(x))dx
derivative of f(x)=\sqrt[4]{x}	derivative\:f(x)=\sqrt[4]{x}
integral of x^5\sqrt[3]{x^3+1}	\int\:x^{5}\sqrt[3]{x^{3}+1}dx
derivative of y=x+2/x	derivative\:y=x+\frac{2}{x}
limit as x approaches 5+of sqrt(x-5)	\lim\:_{x\to\:5+}(\sqrt{x-5})
inverse oflaplace 1/((s+3)^3)	inverselaplace\:\frac{1}{(s+3)^{3}}

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