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Popular Calculus Problems

integral of 1+ln(x)	\int\:1+\ln(x)dx
limit as x approaches 0+of 1/x*sin(x^2)	\lim\:_{x\to\:0+}(\frac{1}{x}\cdot\:\sin(x^{2}))
integral from 0 to pi of x*sin(x)	\int\:_{0}^{π}x\cdot\:\sin(x)dx
sum from n=1 to infinity}3^{-2-2n of*2^{3n+1}	\sum\:_{n=1}^{\infty\:}3^{-2-2n}\cdot\:2^{3n+1}
(\partial)/(\partial x)(x/(2sqrt(2)))	\frac{\partial\:}{\partial\:x}(\frac{x}{2\sqrt{2}})
integral of sqrt(3-2x)x^2	\int\:\sqrt{3-2x}x^{2}dx
area x=7y^2,x=5+2y^2	area\:x=7y^{2},x=5+2y^{2}
tangent of f(x)=4sqrt(x),\at x=25	tangent\:f(x)=4\sqrt{x},\at\:x=25
(\partial)/(\partial x)((t+1)^3)	\frac{\partial\:}{\partial\:x}((t+1)^{3})
derivative of sin(cos(x^2))	\frac{d}{dx}(\sin(\cos(x^{2})))
integral of (2x^2+3)/((x^2+1)^2)	\int\:\frac{2x^{2}+3}{(x^{2}+1)^{2}}dx
(x+y)(dy)/(dx)=x-y	(x+y)\frac{dy}{dx}=x-y
integral of sec^4(x)tan^3(x)	\int\:\sec^{4}(x)\tan^{3}(x)dx
inverse oflaplace (1-2s)/(5s^2+8s+10)	inverselaplace\:\frac{1-2s}{5s^{2}+8s+10}
y^'=t+ty^2	y^{\prime\:}=t+ty^{2}
tangent of f(x)=x+sqrt(x),\at x=4	tangent\:f(x)=x+\sqrt{x},\at\:x=4
integral from-1 to 4 of (x^2+2x-1)	\int\:_{-1}^{4}(x^{2}+2x-1)dx
derivative of-yx	\frac{d}{dx}(-yx)
49y^{''}+140y^'+100y=0	49y^{\prime\:\prime\:}+140y^{\prime\:}+100y=0
derivative of sqrt(x^2+3)	derivative\:\sqrt{x^{2}+3}
integral of (3-x^2)2^x	\int\:(3-x^{2})2^{x}dx
tangent of ln(xy)+y^2=2y,(e,1)	tangent\:\ln(xy)+y^{2}=2y,(e,1)
(\partial)/(\partial x)(y^4 1/x)	\frac{\partial\:}{\partial\:x}(y^{4}\frac{1}{x})
integral of sqrt(x)sin(1+x^{3/2})	\int\:\sqrt{x}\sin(1+x^{\frac{3}{2}})dx
integral of sin(6pix)	\int\:\sin(6πx)dx
(\partial)/(\partial x)(ln(2/x))	\frac{\partial\:}{\partial\:x}(\ln(\frac{2}{x}))
x^2y^{''}+xy^'-y=2x	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-y=2x
derivative of-6/(x^7)	derivative\:-\frac{6}{x^{7}}
integral of 1/((x-1)(x-3))	\int\:\frac{1}{(x-1)(x-3)}dx
derivative of sin(3/x)	\frac{d}{dx}(\sin(\frac{3}{x}))
limit as x approaches 2 of x/(x+2)	\lim\:_{x\to\:2}(\frac{x}{x+2})
derivative of (x^2+1^3)	\frac{d}{dx}((x^{2}+1)^{3})
limit as x approaches-infinity of (4e^{1/x}-1)/(1+e^x)	\lim\:_{x\to\:-\infty\:}(\frac{4e^{\frac{1}{x}}-1}{1+e^{x}})
derivative of \sqrt[5]{x^2+1}	\frac{d}{dx}(\sqrt[5]{x^{2}+1})
derivative of y=cos(x)sin(x)	derivative\:y=\cos(x)\sin(x)
integral of 2/(x^2-3x+2)	\int\:\frac{2}{x^{2}-3x+2}dx
(\partial)/(\partial x)(cos(x+8y))	\frac{\partial\:}{\partial\:x}(\cos(x+8y))
integral from 0 to ln(2) of (e^{3x})/(1+e^{6x)}	\int\:_{0}^{\ln(2)}\frac{e^{3x}}{1+e^{6x}}dx
x*(dy)/(dx)+2y=3	x\cdot\:\frac{dy}{dx}+2y=3
derivative of 5-\|x-5\|	\frac{d}{dx}(5-\left\|x-5\right\|)
(\partial)/(\partial o)(rcos(o))	\frac{\partial\:}{\partial\:o}(r\cos(o))
(\partial)/(\partial x)(-36ysin(9x))	\frac{\partial\:}{\partial\:x}(-36y\sin(9x))
(\partial)/(\partial x)(3x-2y^4)	\frac{\partial\:}{\partial\:x}(3x-2y^{4})
limit as x approaches 2+of (-3)/(x-2)	\lim\:_{x\to\:2+}(\frac{-3}{x-2})
limit as x approaches-5-of (x+3)/(x+5)	\lim\:_{x\to\:-5-}(\frac{x+3}{x+5})
y^'-xy=x^2e^{(x^2)/2}	y^{\prime\:}-xy=x^{2}e^{\frac{x^{2}}{2}}
integral of-(3x^2}{32}+\frac{3x)/8	\int\:-\frac{3x^{2}}{32}+\frac{3x}{8}dx
derivative of y=(2x+1)/(3x-4)	derivative\:y=\frac{2x+1}{3x-4}
derivative of e^{-x/4}	\frac{d}{dx}(e^{-\frac{x}{4}})
integral of ((x^2))/(sqrt(49-x^2))	\int\:\frac{(x^{2})}{\sqrt{49-x^{2}}}dx
y^{''}-9y=2t^2+3t+9	y^{\prime\:\prime\:}-9y=2t^{2}+3t+9
derivative of 3x^2+e^{2x}+pi^2	\frac{d}{dx}(3x^{2}+e^{2x}+π^{2})
sum from n=1 to infinity of n/(6n^2-5)	\sum\:_{n=1}^{\infty\:}\frac{n}{6n^{2}-5}
limit as x approaches+4-of (2x)/(16-x^2)	\lim\:_{x\to\:+4-}(\frac{2x}{16-x^{2}})
y^'=y^2(1+x^3)	y^{\prime\:}=y^{2}(1+x^{3})
integral of (3x+2e^x)^2	\int\:(3x+2e^{x})^{2}dx
(\partial)/(\partial x)(5sqrt(9x^2+16y^2))	\frac{\partial\:}{\partial\:x}(5\sqrt{9x^{2}+16y^{2}})
integral of 7/(x(x^2+25))	\int\:\frac{7}{x(x^{2}+25)}dx
(d^2)/(dx^2)(sin(x^2))	\frac{d^{2}}{dx^{2}}(\sin(x^{2}))
integral of csc^4(x)cot^2(x)	\int\:\csc^{4}(x)\cot^{2}(x)dx
limit as x approaches 2 of 5x^3+x	\lim\:_{x\to\:2}(5x^{3}+x)
derivative of (xsin(x)/(2+cos(x)))	\frac{d}{dx}(\frac{x\sin(x)}{2+\cos(x)})
limit as x approaches 0+of ln(1)	\lim\:_{x\to\:0+}(\ln(1))
derivative of ((4x^5+4x^4-3x^3))/(x^4)	derivative\:\frac{(4x^{5}+4x^{4}-3x^{3})}{x^{4}}
derivative of y=4+sqrt(x-9)	derivative\:y=4+\sqrt{x-9}
y^3(dy)/(dx)=(y^4+1)cos(x)	y^{3}\frac{dy}{dx}=(y^{4}+1)\cos(x)
tangent of f(x)= 6/(sqrt(x))	tangent\:f(x)=\frac{6}{\sqrt{x}}
integral of sqrt(3t)	\int\:\sqrt{3t}dt
laplacetransform e^{-2t}*(t^2+4t+5)	laplacetransform\:e^{-2t}\cdot\:(t^{2}+4t+5)
(\partial)/(\partial x)(1/(f(x)^'(f(x)^{-1)(x))})	\frac{\partial\:}{\partial\:x}(\frac{1}{f(x)^{\prime\:}(f(x)^{-1}(x))})
(\partial)/(\partial x)(y/(2x)-1)	\frac{\partial\:}{\partial\:x}(\frac{y}{2x}-1)
(\partial)/(\partial x)(2pisqrt(x/y))	\frac{\partial\:}{\partial\:x}(2π\sqrt{\frac{x}{y}})
2ydx=3xdy	2ydx=3xdy
sum from n=1 to infinity of 1/(2+3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{2+3^{n}}
ty^'+(2t^2+1)y=3t	ty^{\prime\:}+(2t^{2}+1)y=3t
area x,-1,2	area\:x,-1,2
integral of 1/(z^3sqrt(z^2-36))	\int\:\frac{1}{z^{3}\sqrt{z^{2}-36}}dz
derivative of f(x)=e^4	derivative\:f(x)=e^{4}
integral of (1+cos(4x))/2	\int\:\frac{1+\cos(4x)}{2}dx
integral of 13ycos(3x)+3sin(y)	\int\:13y\cos(3x)+3\sin(y)dx
limit as x approaches 0 of-e^{-λx}	\lim\:_{x\to\:0}(-e^{-λx})
derivative of (4e^x/((4-3e^x)^2))	\frac{d}{dx}(\frac{4e^{x}}{(4-3e^{x})^{2}})
y^'-y^2-1=0,y(0)=1	y^{\prime\:}-y^{2}-1=0,y(0)=1
integral of 7sec^6(t)	\int\:7\sec^{6}(t)dt
implicit (dy)/(dx),x=ye^y	implicit\:\frac{dy}{dx},x=ye^{y}
sum from n=1 to infinity of 3(-2/3)^n	\sum\:_{n=1}^{\infty\:}3(-\frac{2}{3})^{n}
(dy)/(dx)=(2+y^2)/(2xy),y(1)=1	\frac{dy}{dx}=\frac{2+y^{2}}{2xy},y(1)=1
integral of xsqrt(x^2+3)	\int\:x\sqrt{x^{2}+3}dx
integral of x/(sqrt(-x^2+5))	\int\:\frac{x}{\sqrt{-x^{2}+5}}dx
integral from 0 to 3/2 of xcos(pix)	\int\:_{0}^{\frac{3}{2}}x\cos(πx)dx
derivative of-1/(2x^2)	derivative\:-\frac{1}{2x^{2}}
limit as x approaches infinity of (sqrt(x^3+20x))/(10x-2)	\lim\:_{x\to\:\infty\:}(\frac{\sqrt{x^{3}+20x}}{10x-2})
(\partial)/(\partial x)(cos(x)sin(yz))	\frac{\partial\:}{\partial\:x}(\cos(x)\sin(yz))
derivative of 139+(36/x+(x^2)/(16))	\frac{d}{dx}(139+\frac{36}{x}+\frac{x^{2}}{16})
integral of (x^2)/(5+x)	\int\:\frac{x^{2}}{5+x}dx
integral of 13log_{15}(x)	\int\:13\log_{15}(x)dx
integral of (x^2+x)*e^{2x}	\int\:(x^{2}+x)\cdot\:e^{2x}dx
integral of-(e^{2x})/(1+e^x)	\int\:-\frac{e^{2x}}{1+e^{x}}dx
limit as x approaches 0+of (tan(6x))^x	\lim\:_{x\to\:0+}((\tan(6x))^{x})
(dy)/(dx)=x(x-1)	\frac{dy}{dx}=x(x-1)

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