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Popular Calculus Problems

limit as x approaches 1 of (x^2+x)/(x+1)	\lim\:_{x\to\:1}(\frac{x^{2}+x}{x+1})
integral of θ^3cos(θ^2)	\int\:θ^{3}\cos(θ^{2})dθ
derivative of (2x+1/(x+3))	\frac{d}{dx}(\frac{2x+1}{x+3})
(dy)/(dt)=ty+t	\frac{dy}{dt}=ty+t
(dy)/(dx)= 1/2 x+4	\frac{dy}{dx}=\frac{1}{2}x+4
(dy)/(dx)+xy= x/(y^3)	\frac{dy}{dx}+xy=\frac{x}{y^{3}}
integral of 7/(x^2-6x+25)	\int\:\frac{7}{x^{2}-6x+25}dx
area x^2+2x,1,2	area\:x^{2}+2x,1,2
integral from-2 to 2 of (16)/(x^2-4x-60)	\int\:_{-2}^{2}\frac{16}{x^{2}-4x-60}dx
y^{'''}+y^'=x	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=x
derivative of (x-1e^x)	\frac{d}{dx}((x-1)e^{x})
inverse oflaplace 7/(s^2+42)	inverselaplace\:\frac{7}{s^{2}+42}
derivative of 1-ln^2(x)	\frac{d}{dx}(1-\ln^{2}(x))
(\partial)/(\partial x)(x^2-7xy+y)	\frac{\partial\:}{\partial\:x}(x^{2}-7xy+y)
integral of csc^2(x/5)	\int\:\csc^{2}(\frac{x}{5})dx
(\partial)/(\partial x)(sin(x^2-7xy))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}-7xy))
integral from 0 to infinity of e^{-x}x	\int\:_{0}^{\infty\:}e^{-x}xdx
(\partial)/(\partial z)(sin(x))	\frac{\partial\:}{\partial\:z}(\sin(x))
(\partial)/(\partial x)(e^{-8y}sin(8x))	\frac{\partial\:}{\partial\:x}(e^{-8y}\sin(8x))
derivative of {f}(x(x{f}(x)(x{f}(x))))	\frac{d}{dx}({f}(x)(x{f}(x)(x{f}(x))))
derivative of 3^{xln(x})	\frac{d}{dx}(3^{x\ln(x)})
derivative of log_{e}(sin(2x)+cot(2x))	derivative\:\log_{e}(\sin(2x)+\cot(2x))
derivative of y= 1/2 x	derivative\:y=\frac{1}{2}x
integral from pi to 2pi of (t-pi)e^{-st}	\int\:_{π}^{2π}(t-π)e^{-st}dt
xy^'-2y=x^5	xy^{\prime\:}-2y=x^{5}
derivative of 13-x^2	derivative\:13-x^{2}
(\partial)/(\partial y)(3arctan(x/y))	\frac{\partial\:}{\partial\:y}(3\arctan(\frac{x}{y}))
(\partial)/(\partial y)(-sin(xy)y)	\frac{\partial\:}{\partial\:y}(-\sin(xy)y)
integral of (1-2x)^{3/2}	\int\:(1-2x)^{\frac{3}{2}}dx
limit as x approaches 0 of sqrt(x^2-x^4)	\lim\:_{x\to\:0}(\sqrt{x^{2}-x^{4}})
(\partial)/(\partial x)(6xy-2+10x^2y^2)	\frac{\partial\:}{\partial\:x}(6xy-2+10x^{2}y^{2})
(\partial)/(\partial x)(xarctan(y+z))	\frac{\partial\:}{\partial\:x}(x\arctan(y+z))
tangent of f(x)= x/(-6x+6),\at x=2	tangent\:f(x)=\frac{x}{-6x+6},\at\:x=2
derivative of (x^2-3x+1/(sqrt(x)))	\frac{d}{dx}(\frac{x^{2}-3x+1}{\sqrt{x}})
limit as x approaches 5 of 1/((x-5)^2)	\lim\:_{x\to\:5}(\frac{1}{(x-5)^{2}})
integral of (x^2)/(2sqrt(1-x^2))	\int\:\frac{x^{2}}{2\sqrt{1-x^{2}}}dx
derivative of x/(2pi)	\frac{d}{dx}(\frac{x}{2π})
integral of ((x^2))/(sqrt(5+2x^3))	\int\:\frac{(x^{2})}{\sqrt{5+2x^{3}}}dx
integral of b/(sqrt(b^2-2b+2))	\int\:\frac{b}{\sqrt{b^{2}-2b+2}}
integral of 3x^2(x^3+8)^5	\int\:3x^{2}(x^{3}+8)^{5}dx
derivative of y=-2sin(x^2)	derivative\:y=-2\sin(x^{2})
integral of (2x^2+1)e^{x^2}	\int\:(2x^{2}+1)e^{x^{2}}dx
integral of e^{6t}cos(2t)	\int\:e^{6t}\cos(2t)dt
integral from 0 to 2pi of 3sin(2t)	\int\:_{0}^{2π}3\sin(2t)dt
derivative of ln((8x/(x+5)))	\frac{d}{dx}(\ln(\frac{8x}{x+5}))
limit as x approaches 5 of 1/((x-5)^3)	\lim\:_{x\to\:5}(\frac{1}{(x-5)^{3}})
(\partial)/(\partial x)((e^x)/(y+x^8))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{y+x^{8}})
derivative of (x+y/(xy))	\frac{d}{dx}(\frac{x+y}{xy})
y^'=1-y/(20)	y^{\prime\:}=1-\frac{y}{20}
7x^2y^'=y^'+9xe-y	7x^{2}y^{\prime\:}=y^{\prime\:}+9xe-y
integral from 1 to infinity of 1/(x^2+x)	\int\:_{1}^{\infty\:}\frac{1}{x^{2}+x}dx
derivative of 2^xln^2(2)	\frac{d}{dx}(2^{x}\ln^{2}(2))
area 9x+11,7x+14,[23,13]	area\:9x+11,7x+14,[23,13]
(\partial)/(\partial y)(e^ysin(x))	\frac{\partial\:}{\partial\:y}(e^{y}\sin(x))
(d^2)/(dx^2)(x\sqrt[3]{x})	\frac{d^{2}}{dx^{2}}(x\sqrt[3]{x})
inverse oflaplace ((4s-18))/(s^2-6s+10)	inverselaplace\:\frac{(4s-18)}{s^{2}-6s+10}
(dy)/(dt)=-3y+4cos(2t)	\frac{dy}{dt}=-3y+4\cos(2t)
(7xy^2-2y)+(7x^2y-2x)y^'=0	(7xy^{2}-2y)+(7x^{2}y-2x)y^{\prime\:}=0
integral of 20x	\int\:20xdx
integral of (x+1)/((2-x)^2)	\int\:\frac{x+1}{(2-x)^{2}}dx
integral from 0 to 4 of (e^{-2x}+1)	\int\:_{0}^{4}(e^{-2x}+1)dx
derivative of y^x	\frac{d}{dx}(y^{x})
derivative of f(x)=7x+6	derivative\:f(x)=7x+6
integral of 1/(2sqrt(tan(x)))	\int\:\frac{1}{2\sqrt{\tan(x)}}dx
inverse oflaplace (s^2+3s+5)/(s^3(s+2))	inverselaplace\:\frac{s^{2}+3s+5}{s^{3}(s+2)}
(dy)/(dx)=sqrt(x)	\frac{dy}{dx}=\sqrt{x}
sum from n=0 to infinity of 2/(n^2)	\sum\:_{n=0}^{\infty\:}\frac{2}{n^{2}}
integral from-4 to 2 of (x+4)	\int\:_{-4}^{2}(x+4)dx
area y^2=4x,y=x^2	area\:y^{2}=4x,y=x^{2}
tangent of 8x^2-2,\at x=-4	tangent\:8x^{2}-2,\at\:x=-4
tangent of x^4+2x^2+3,\at x=-2	tangent\:x^{4}+2x^{2}+3,\at\:x=-2
f(x)=4e^{2x^3}	f(x)=4e^{2x^{3}}
integral from-infinity to 0 of 1/(7-4x)	\int\:_{-\infty\:}^{0}\frac{1}{7-4x}dx
integral of x^2e^{-5x}	\int\:x^{2}e^{-5x}dx
(\partial}{\partial x}(\frac{y+1)/x)	\frac{\partial\:}{\partial\:x}(\frac{y+1}{x})
derivative of 3/((1-x^2))	\frac{d}{dx}(\frac{3}{(1-x)^{2}})
integral of (3x^5-6sqrt(x)+e^x-4/x)	\int\:(3x^{5}-6\sqrt{x}+e^{x}-\frac{4}{x})dx
(\partial)/(\partial x)(xcos(y)-ycos(x))	\frac{\partial\:}{\partial\:x}(x\cos(y)-y\cos(x))
derivative of g(x)=ln(xe^{-2x})	derivative\:g(x)=\ln(xe^{-2x})
integral of (x^4+10x^3)/(2x^2)	\int\:\frac{x^{4}+10x^{3}}{2x^{2}}dx
integral of 2(1-3x)^2	\int\:2(1-3x)^{2}dx
derivative of (x^3-2^2)	\frac{d}{dx}((x^{3}-2)^{2})
integral of 1/(e^{-x)+e^x}	\int\:\frac{1}{e^{-x}+e^{x}}dx
limit as t approaches 0+of 4/t-1/(e^t-1)	\lim\:_{t\to\:0+}(\frac{4}{t}-\frac{1}{e^{t}-1})
derivative of 2csc(xcot(x))	\frac{d}{dx}(2\csc(x)\cot(x))
tangent of y=2sqrt(x)+1,\at x= 1/4	tangent\:y=2\sqrt{x}+1,\at\:x=\frac{1}{4}
inverse oflaplace (s^2)/((s-3)(s^2+5))	inverselaplace\:\frac{s^{2}}{(s-3)(s^{2}+5)}
sum from n=0 to infinity of (e^n)/(n^2)	\sum\:_{n=0}^{\infty\:}\frac{e^{n}}{n^{2}}
(\partial)/(\partial z)(2xz^3e^{y^2})	\frac{\partial\:}{\partial\:z}(2xz^{3}e^{y^{2}})
derivative of f(x)=t^4cos(t)	derivative\:f(x)=t^{4}\cos(t)
integral from 5 to 9 of x^2	\int\:_{5}^{9}x^{2}dx
limit as x approaches 2 of 2x+6	\lim\:_{x\to\:2}(2x+6)
area 5-x^2,17-7x	area\:5-x^{2},17-7x
integral of ct	\int\:ctdt
limit as x approaches pi of cos(x)	\lim\:_{x\to\:π}(\cos(x))
derivative of 2/((x+2)^2)	derivative\:\frac{2}{(x+2)^{2}}
integral of (4/x+2e^x-sin(x))	\int\:(\frac{4}{x}+2e^{x}-\sin(x))dx
tangent of y=2x^3-3x+1,(1,0)	tangent\:y=2x^{3}-3x+1,(1,0)
derivative of sqrt(x^2+6x+9)	derivative\:\sqrt{x^{2}+6x+9}
derivative of 4ln(9-5x^2)	derivative\:4\ln(9-5x^{2})

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