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Popular Calculus Problems

integral from 0 to 8pi of sqrt(5+t^2)	\int\:_{0}^{8π}\sqrt{5+t^{2}}dt
derivative of x/(e^x)	derivative\:\frac{x}{e^{x}}
laplacetransform f(t)=cos(t)	laplacetransform\:f(t)=\cos(t)
sum from n=0 to infinity of (10^n)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{10^{n}}{n!}
y^'=-5y^2	y^{\prime\:}=-5y^{2}
f(x)=arctan(7x)	f(x)=\arctan(7x)
f(x)=csc(x)cot(x)	f(x)=\csc(x)\cot(x)
(x/(2y^4))dx+((3y^2-x^2)/(y^5))dy=0	(\frac{x}{2y^{4}})dx+(\frac{3y^{2}-x^{2}}{y^{5}})dy=0
derivative of 5x^2+2x	\frac{d}{dx}(5x^{2}+2x)
integral of sqrt(x)ln(3x)	\int\:\sqrt{x}\ln(3x)dx
integral of (5x^2)/((144+x^2)^2)	\int\:\frac{5x^{2}}{(144+x^{2})^{2}}dx
integral of (x^2)/(e^{(x^3))}	\int\:\frac{x^{2}}{e^{(x^{3})}}dx
limit as x approaches 0+of (4x)/(sin(x))	\lim\:_{x\to\:0+}(\frac{4x}{\sin(x)})
(dy)/(dx)-y=e^xy^2	\frac{dy}{dx}-y=e^{x}y^{2}
slope of (-17,-5),(2,-18)	slope\:(-17,-5),(2,-18)
derivative of y=(7x-1)	derivative\:y=(7x-1)
derivative of log_{8}(x)	derivative\:\log_{8}(x)
integral of (3x^2-2x+5)/((x+3)^3)	\int\:\frac{3x^{2}-2x+5}{(x+3)^{3}}dx
derivative of ((x^2+1/(2x-1))^2)	\frac{d}{dx}((\frac{x^{2}+1}{2x-1})^{2})
derivative of (9(x-3)/((x-1)^3))	\frac{d}{dx}(\frac{9(x-3)}{(x-1)^{3}})
limit as x approaches 5-of 1/(x^2-25)	\lim\:_{x\to\:5-}(\frac{1}{x^{2}-25})
(\partial)/(\partial t)((3s+t)/(4s-t))	\frac{\partial\:}{\partial\:t}(\frac{3s+t}{4s-t})
2ycos(x)dx+3sin(x)dy=0	2y\cos(x)dx+3\sin(x)dy=0
e^xy(dy)/(dx)=e^{-y}+e^{-2x-y}	e^{x}y\frac{dy}{dx}=e^{-y}+e^{-2x-y}
y^'+5x^4y=x^4	y^{\prime\:}+5x^{4}y=x^{4}
integral of y/(sqrt(x^2+y^2))	\int\:\frac{y}{\sqrt{x^{2}+y^{2}}}dy
(\partial)/(\partial x)(xy^2-yx^3)	\frac{\partial\:}{\partial\:x}(xy^{2}-yx^{3})
derivative of 1+40x^3-3x^5	\frac{d}{dx}(1+40x^{3}-3x^{5})
limit as x approaches 2 of 1680x^3-120x	\lim\:_{x\to\:2}(1680x^{3}-120x)
integral of (2x-5)/(x^2+2x+2)	\int\:\frac{2x-5}{x^{2}+2x+2}dx
integral of 1/(8x)	\int\:\frac{1}{8x}dx
sum from n=0 to infinity of 1/n x^n	\sum\:_{n=0}^{\infty\:}\frac{1}{n}x^{n}
integral of sec^3(z)	\int\:\sec^{3}(z)dz
derivative of sin((pix/3))	\frac{d}{dx}(\sin(\frac{πx}{3}))
f(x)=ln(x^2+x+1)	f(x)=\ln(x^{2}+x+1)
y^{''''}-y=0	y^{\prime\:\prime\:\prime\:\prime\:}-y=0
integral of x^{-1}	\int\:x^{-1}dx
integral from 0 to 2 of e^{-t}	\int\:_{0}^{2}e^{-t}dt
limit as x approaches infinity of 8+5/x	\lim\:_{x\to\:\infty\:}(8+\frac{5}{x})
derivative of-5/((x-2^2))	\frac{d}{dx}(-\frac{5}{(x-2)^{2}})
(\partial)/(\partial y)(y/(y-2x))	\frac{\partial\:}{\partial\:y}(\frac{y}{y-2x})
(dv)/(dt)=9.8-v/5 ,v(0)=0	\frac{dv}{dt}=9.8-\frac{v}{5},v(0)=0
derivative of-2sqrt(7s^2+8)	derivative\:-2\sqrt{7s^{2}+8}
xy^'=x+y	xy^{\prime\:}=x+y
derivative of (Kx+11/(x^2+(K+1)x+11))	\frac{d}{dx}(\frac{Kx+11}{x^{2}+(K+1)x+11})
integral of sin(9x)cos(5x)	\int\:\sin(9x)\cos(5x)dx
limit as x approaches 0 of 8xcot(3x)	\lim\:_{x\to\:0}(8x\cot(3x))
sum from n=1 to infinity of ((n+1)/n)^n	\sum\:_{n=1}^{\infty\:}(\frac{n+1}{n})^{n}
y^{''}-2y^'+y=xe^{-x}	y^{\prime\:\prime\:}-2y^{\prime\:}+y=xe^{-x}
(\partial)/(\partial z)(x^ay^bz^c)	\frac{\partial\:}{\partial\:z}(x^{a}y^{b}z^{c})
(dy)/(dx)=((y-1))/(x+3)	\frac{dy}{dx}=\frac{(y-1)}{x+3}
y^'+y/x =7x^3y^2	y^{\prime\:}+\frac{y}{x}=7x^{3}y^{2}
tangent of sqrt(3)^x	tangent\:\sqrt{3}^{x}
derivative of e^{3x}sin(x)	\frac{d}{dx}(e^{3x}\sin(x))
integral of x^2(1-x^3)^4	\int\:x^{2}(1-x^{3})^{4}dx
inverse oflaplace (s^2-2s+3)/((s-2)^3)	inverselaplace\:\frac{s^{2}-2s+3}{(s-2)^{3}}
integral of (5x+3)/(x^2-9)	\int\:\frac{5x+3}{x^{2}-9}dx
integral of x^3sin(6x)	\int\:x^{3}\sin(6x)dx
tangent of f(x)=x^2-1/x	tangent\:f(x)=x^{2}-\frac{1}{x}
derivative of 1-1/(1+x)	\frac{d}{dx}(1-\frac{1}{1+x})
(\partial)/(\partial x)((4x-4z)/(3y+4z))	\frac{\partial\:}{\partial\:x}(\frac{4x-4z}{3y+4z})
integral of cos^2(1/2)x	\int\:\cos^{2}(\frac{1}{2})xdx
inverse oflaplace (3s)/((s-1)(s^2-4))	inverselaplace\:\frac{3s}{(s-1)(s^{2}-4)}
integral of ((6x-7))/(3x^2-7x+11)	\int\:\frac{(6x-7)}{3x^{2}-7x+11}dx
slope of (2,-3),(-1,15)	slope\:(2,-3),(-1,15)
(\partial)/(\partial x)(x^5+3x^3y^2+3xy^4)	\frac{\partial\:}{\partial\:x}(x^{5}+3x^{3}y^{2}+3xy^{4})
limit as x approaches 1 of (x^2)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{2}}{x-1})
(\partial)/(\partial y)(xy^2+x^2y)	\frac{\partial\:}{\partial\:y}(xy^{2}+x^{2}y)
(\partial)/(\partial x)(x^2y-x^3)	\frac{\partial\:}{\partial\:x}(x^{2}y-x^{3})
(\partial)/(\partial x)(6xy^2-2x^3-3y^4)	\frac{\partial\:}{\partial\:x}(6xy^{2}-2x^{3}-3y^{4})
(d^2y)/(dx^2)=3	\frac{d^{2}y}{dx^{2}}=3
(\partial)/(\partial x)(sqrt(2x+4y))	\frac{\partial\:}{\partial\:x}(\sqrt{2x+4y})
derivative of 2x*e^x	\frac{d}{dx}(2x\cdot\:e^{x})
integral of 1/(4sin(x))	\int\:\frac{1}{4\sin(x)}dx
limit as x approaches 0 of log_{2/3}(x)	\lim\:_{x\to\:0}(\log_{\frac{2}{3}}(x))
(\partial)/(\partial x)(5e^{xy+6})	\frac{\partial\:}{\partial\:x}(5e^{xy+6})
y^{''}+2y^'+y=6e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=6e^{-t}
integral of 1/4 e^{-2x}	\int\:\frac{1}{4}e^{-2x}dx
derivative of f(x)=4x^2-5x+2	derivative\:f(x)=4x^{2}-5x+2
taylor ln(2/(2-x))	taylor\:\ln(\frac{2}{2-x})
derivative of x^2e^{-1/x}	\frac{d}{dx}(x^{2}e^{-\frac{1}{x}})
maclaurin 1/(1+x^2),x=2	maclaurin\:\frac{1}{1+x^{2}},x=2
limit as x approaches-9-of (x+10)/(x+9)	\lim\:_{x\to\:-9-}(\frac{x+10}{x+9})
(\partial)/(\partial x)(x^ny 1/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(x^{n}y\frac{1}{x^{2}+y^{2}})
integral of (1-x^3)^2	\int\:(1-x^{3})^{2}dx
derivative of-4e^x-sin(x-9)	\frac{d}{dx}(-4e^{x}-\sin(x)-9)
integral of pi^2	\int\:π^{2}
integral of 4sin^2(x)cos^2(x)	\int\:4\sin^{2}(x)\cos^{2}(x)dx
integral of (2x+1)/(x^2-1)	\int\:\frac{2x+1}{x^{2}-1}dx
integral of csc^3(x	\int\:\csc^{3}(d)xdx
integral from 0 to 1 of x^4e^x	\int\:_{0}^{1}x^{4}e^{x}dx
integral of (26)/((1-x^2)^{3/2)}	\int\:\frac{26}{(1-x^{2})^{\frac{3}{2}}}dx
(\partial)/(\partial y)(sin(xy^2+y)+2e^x)	\frac{\partial\:}{\partial\:y}(\sin(xy^{2}+y)+2e^{x})
sum from n=1 to infinity of (1+5^n)/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{1+5^{n}}{7^{n}}
derivative of e^{3x}y	\frac{d}{dx}(e^{3x}y)
integral of x^{-3.5}	\int\:x^{-3.5}dx
sum from n=1.0E22 to infinity of 1/(n^2)	\sum\:_{n=1.0E22}^{\infty\:}\frac{1}{n^{2}}
tangent of f(x)=xe^{-x},\at x=2	tangent\:f(x)=xe^{-x},\at\:x=2
inverse oflaplace ((s+1))/(s+2)	inverselaplace\:\frac{(s+1)}{s+2}
tangent of y=3sec(x)	tangent\:y=3\sec(x)

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