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Popular Calculus Problems

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}
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}})
integral from 5 to 9 of x^2	\int\:_{5}^{9}x^{2}dx
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})
(x^2+1)dy=(x-4xy)dx	(x^{2}+1)dy=(x-4xy)dx
integral of 22tan^3(x)	\int\:22\tan^{3}(x)dx
integral of 1/(sqrt(1+e^x))	\int\:\frac{1}{\sqrt{1+e^{x}}}dx
integral of (e^x)/(e^x+8)	\int\:\frac{e^{x}}{e^{x}+8}dx
integral from 0 to 1 of 4/(sqrt(x)(1+x))	\int\:_{0}^{1}\frac{4}{\sqrt{x}(1+x)}dx
derivative of 7/(xln(x))	\frac{d}{dx}(\frac{7}{x\ln(x)})
(\partial)/(\partial y)(x^2+z^2)	\frac{\partial\:}{\partial\:y}(x^{2}+z^{2})
(\partial)/(\partial x)(a)	\frac{\partial\:}{\partial\:x}(a)
f(x)=(((x-3))/((x+2)))^2x=-1	f(x)=(\frac{(x-3)}{(x+2)})^{2}x=-1
integral of (e^x)/((e^x+1)^3)	\int\:\frac{e^{x}}{(e^{x}+1)^{3}}dx
y^'=ry(1-y/k)	y^{\prime\:}=ry(1-\frac{y}{k})
derivative of (x^3-2^5)	\frac{d}{dx}((x^{3}-2)^{5})
limit as x approaches 0 of x^{14}ln(x)	\lim\:_{x\to\:0}(x^{14}\ln(x))
derivative of e^{3/2 x}	\frac{d}{dx}(e^{\frac{3}{2}x})
derivative of 1/((x-5^2))	\frac{d}{dx}(\frac{1}{(x-5)^{2}})
integral of (te^ti-4e^{-2t}j+8te^{t^2}k)	\int\:(te^{t}i-4e^{-2t}j+8te^{t^{2}}k)dt
slope of (90,62536),(950,9000)	slope\:(90,62536),(950,9000)
(\partial)/(\partial x)(y^2(x+y)^{-2})	\frac{\partial\:}{\partial\:x}(y^{2}(x+y)^{-2})
11xy^'+y=132x	11xy^{\prime\:}+y=132x
integral of e^{-x}+2	\int\:e^{-x}+2dx
derivative of (9x/((x^2+81)^{3/2)})	\frac{d}{dx}(\frac{9x}{(x^{2}+81)^{\frac{3}{2}}})
derivative of ((x-1/(x+1))^3)	\frac{d}{dx}((\frac{x-1}{x+1})^{3})
integral of 5x^{15}e^{-x^8}	\int\:5x^{15}e^{-x^{8}}dx
integral of 1/(x(ln(x))^6)	\int\:\frac{1}{x(\ln(x))^{6}}dx
inverse oflaplace (4s)/((s+1)^2)	inverselaplace\:\frac{4s}{(s+1)^{2}}
derivative of 3x^2+e^2x+pi^2	\frac{d}{dx}(3x^{2}+e^{2}x+π^{2})
derivative of f(x)=x^8-9e^{3x}	derivative\:f(x)=x^{8}-9e^{3x}
integral from 0 to pi of cos(t)	\int\:_{0}^{π}\cos(t)dt
derivative of 2x^3-12x^2+18x	\frac{d}{dx}(2x^{3}-12x^{2}+18x)
limit as x approaches 3 of (-4)x	\lim\:_{x\to\:3}((-4)x)
(dx)/(dy)+800y=400	\frac{dx}{dy}+800y=400
derivative of (x-3(x^3-2))	\frac{d}{dx}((x-3)(x^{3}-2))
derivative of (ln(5x)^2)	\frac{d}{dx}((\ln(5x))^{2})
(\partial)/(\partial x)((90-x)^2*(x+2))	\frac{\partial\:}{\partial\:x}((90-x)^{2}\cdot\:(x+2))
integral of 3/(2xsqrt(9x^2-1))	\int\:\frac{3}{2x\sqrt{9x^{2}-1}}dx
derivative of f(x)=14^x	derivative\:f(x)=14^{x}
integral from 1 to 4 of 1/(x-4)	\int\:_{1}^{4}\frac{1}{x-4}dx
laplacetransform 4t-10	laplacetransform\:4t-10
integral of 1/(xsqrt(x^2-4))	\int\:\frac{1}{x\sqrt{x^{2}-4}}dx
integral of (\sqrt[3]{x^2})	\int\:(\sqrt[3]{x^{2}})dx
derivative of ln((7x^2+8x+5)/(8x^3-1))	derivative\:\ln(\frac{7x^{2}+8x+5}{8x^{3}-1})
derivative of f(x)=sqrt(x)e^x\at x	derivative\:f(x)=\sqrt{x}e^{x}\at\:x
integral of \sqrt[8]{x}+\sqrt[9]{x}	\int\:\sqrt[8]{x}+\sqrt[9]{x}dx
derivative of f(x)=(t^6+1)^{500}	derivative\:f(x)=(t^{6}+1)^{500}
tangent of-x/((25-x^2)^{1/2)}	tangent\:-\frac{x}{(25-x^{2})^{\frac{1}{2}}}

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