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Popular Calculus Problems

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})
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}})
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
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
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 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})
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
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)
derivative of 2-1/x	\frac{d}{dx}(2-\frac{1}{x})
integral of (1/(ln(x))+ln(ln(x)))	\int\:(\frac{1}{\ln(x)}+\ln(\ln(x)))dx
derivative of f(x)=log_{7}(xe^x)	derivative\:f(x)=\log_{7}(xe^{x})
integral from 0 to 1 of e^5	\int\:_{0}^{1}e^{5}dx
(\partial)/(\partial y)(zarcsin(y/x))	\frac{\partial\:}{\partial\:y}(z\arcsin(\frac{y}{x}))
integral of (2-t)e^{-st}	\int\:(2-t)e^{-st}dt
limit as x approaches 0 of (ln(1-2x))/x	\lim\:_{x\to\:0}(\frac{\ln(1-2x)}{x})
integral of (2u)/(1-u^2)	\int\:\frac{2u}{1-u^{2}}du
slope ofintercept (-9,5),(-3,3)	slopeintercept\:(-9,5),(-3,3)
derivative of 3^{x-2}	\frac{d}{dx}(3^{x-2})
tangent of f(x)=sqrt(4-x),\at x=0	tangent\:f(x)=\sqrt{4-x},\at\:x=0
(\partial)/(\partial v)(u+v)	\frac{\partial\:}{\partial\:v}(u+v)
derivative of x/(sqrt(x^21))	derivative\:\frac{x}{\sqrt{x^{2}1}}
derivative of-2/((1+x^{3/2)})	\frac{d}{dx}(-\frac{2}{(1+x)^{\frac{3}{2}}})
tangent of f(x)= 7/(x+1),\at x=7	tangent\:f(x)=\frac{7}{x+1},\at\:x=7
integral of cos(x)cos(y)	\int\:\cos(x)\cos(y)dx
integral of 1/(x^{14)}	\int\:\frac{1}{x^{14}}dx
integral of (5x+2)^2	\int\:(5x+2)^{2}dx
y^{''}+10y=0,y(0)=2,y^'(0)=10	y^{\prime\:\prime\:}+10y=0,y(0)=2,y^{\prime\:}(0)=10
integral of tan^7(x)sec^{17}(x)	\int\:\tan^{7}(x)\sec^{17}(x)dx
derivative of s(t)= 1/(t^2+6t-7)	derivative\:s(t)=\frac{1}{t^{2}+6t-7}
integral of (ln(4x))/x	\int\:\frac{\ln(4x)}{x}dx
(\partial)/(\partial x)(-(2y)/(x^2+y^2+1))	\frac{\partial\:}{\partial\:x}(-\frac{2y}{x^{2}+y^{2}+1})
integral of e^{7x}cos(8x)	\int\:e^{7x}\cos(8x)dx
integral from 0 to 2pi of cos(x)	\int\:_{0}^{2π}\cos(x)dx
(\partial)/(\partial x)((4x-5y)^{3/2})	\frac{\partial\:}{\partial\:x}((4x-5y)^{\frac{3}{2}})
integral of 3e^{-0.2x}	\int\:3e^{-0.2x}dx
derivative of \sqrt[4]{(2x+x^5)^7}	derivative\:\sqrt[4]{(2x+x^{5})^{7}}
derivative of sec(5x)	derivative\:\sec(5x)
derivative of f(x)=sqrt(5x^2+5x+7)	derivative\:f(x)=\sqrt{5x^{2}+5x+7}
(\partial)/(\partial x)(arctan(y/((x-1))))	\frac{\partial\:}{\partial\:x}(\arctan(\frac{y}{(x-1)}))
(\partial)/(\partial x)(sqrt(62-2x^2-2y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{62-2x^{2}-2y^{2}})
derivative of ln(1/(1+x))	\frac{d}{dx}(\ln(\frac{1}{1+x}))
f(x)=arcsec(x)	f(x)=\arcsec(x)
y^'+7xe^y=0	y^{\prime\:}+7xe^{y}=0
integral of (e^{x^2})	\int\:(e^{x^{2}})dx
derivative of y=(2x+1)(x-2)^3	derivative\:y=(2x+1)(x-2)^{3}
derivative of-csc^2(x)	derivative\:-\csc^{2}(x)
(dy)/(dx)=sqrt(9x+y)-9	\frac{dy}{dx}=\sqrt{9x+y}-9
integral of (4y^2-6y+x+2)/x	\int\:\frac{4y^{2}-6y+x+2}{x}
y^{''}-2y^'=0	y^{\prime\:\prime\:}-2y^{\prime\:}=0
(\partial)/(\partial x)((x+y)ln(x+y))	\frac{\partial\:}{\partial\:x}((x+y)\ln(x+y))
limit as x approaches 4+of x+1	\lim\:_{x\to\:4+}(x+1)
integral of e^{3x}*sin(2x)	\int\:e^{3x}\cdot\:\sin(2x)dx
(dy)/(dt)=ky^2	\frac{dy}{dt}=ky^{2}

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