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Popular Calculus Problems

integral from 0 to 1 of-5x5^x	\int\:_{0}^{1}-5x5^{x}dx
integral of 3/((x-2)(x^2+4))	\int\:\frac{3}{(x-2)(x^{2}+4)}dx
derivative of (3x/(sqrt(1-x)))	\frac{d}{dx}(\frac{3x}{\sqrt{1-x}})
integral of ((x^{1/3}))/(x^{2/3)}	\int\:\frac{(x^{\frac{1}{3}})}{x^{\frac{2}{3}}}dx
integral of 1/((8-2x-x^2)^{3/2)}	\int\:\frac{1}{(8-2x-x^{2})^{\frac{3}{2}}}dx
sum from n=0 to infinity of (2^n)/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{2^{n}}{4^{n}}
integral of (4x^2-5x)^5(8x-5)	\int\:(4x^{2}-5x)^{5}(8x-5)dx
integral from-infinity to 1 of 2^x	\int\:_{-\infty\:}^{1}2^{x}dx
integral of x(x+1)^9	\int\:x(x+1)^{9}dx
integral of 2sqrt(2x-1)	\int\:2\sqrt{2x-1}dx
integral of 5/((3x-1)^5)	\int\:\frac{5}{(3x-1)^{5}}dx
(\partial)/(\partial x)(4x^2y^3-4)	\frac{\partial\:}{\partial\:x}(4x^{2}y^{3}-4)
y^'=0.2ln((3000)/y)y,y(0)=1000	y^{\prime\:}=0.2\ln(\frac{3000}{y})y,y(0)=1000
integral of (x+2)/(x^2+x+1)	\int\:\frac{x+2}{x^{2}+x+1}dx
derivative of pi^2	\frac{d}{dx}(π^{2})
limit as x approaches 0 of 8e^{-x}tan(x)	\lim\:_{x\to\:0}(8e^{-x}\tan(x))
limit as x approaches-5 of 1/((x^2-25))	\lim\:_{x\to\:-5}(\frac{1}{(x^{2}-25)})
derivative of ln(1/(\sqrt[3]{x}))	\frac{d}{dx}(\ln(\frac{1}{\sqrt[3]{x}}))
derivative of e^{-x}-xe^{-x}	derivative\:e^{-x}-xe^{-x}
(\partial)/(\partial y)(e^{xy^2+z^2})	\frac{\partial\:}{\partial\:y}(e^{xy^{2}+z^{2}})
limit as x approaches 0 of-x+1	\lim\:_{x\to\:0}(-x+1)
x^'=x^2,x(0)=-1	x^{\prime\:}=x^{2},x(0)=-1
integral of 5x^8	\int\:5x^{8}dx
derivative of 2/3 x^9	\frac{d}{dx}(\frac{2}{3}x^{9})
sum from n=-infinity to infinity of 1/n	\sum\:_{n=-\infty\:}^{\infty\:}\frac{1}{n}
derivative of e^{-x}x^2-4e^{-x}x+2e^{-x}	\frac{d}{dx}(e^{-x}x^{2}-4e^{-x}x+2e^{-x})
tangent of f(x)=x^2-5	tangent\:f(x)=x^{2}-5
y^{'''}+2y^{''}+5y^'-26y=0	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}+5y^{\prime\:}-26y=0
tangent of y=(x^2)/2+4x+2,(-3,-11/2)	tangent\:y=\frac{x^{2}}{2}+4x+2,(-3,-\frac{11}{2})
y^'+1/2 y=y^3	y^{\prime\:}+\frac{1}{2}y=y^{3}
derivative of 1/2 e^{-t}cos(t)+1/2 e^{-t}sin(t)-1/2 e^{-2t}	derivative\:\frac{1}{2}e^{-t}\cos(t)+\frac{1}{2}e^{-t}\sin(t)-\frac{1}{2}e^{-2t}
derivative of cos^2(ln(x))	\frac{d}{dx}(\cos^{2}(\ln(x)))
y^{''}+8y^'+6y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+6y=0
inverse oflaplace (4s+3)/(s(s^2+6s+34))	inverselaplace\:\frac{4s+3}{s(s^{2}+6s+34)}
f^'(x)=sqrt(x+1)	f^{\prime\:}(x)=\sqrt{x+1}
derivative of-sin(2x2+cos(2x)2)	\frac{d}{dx}(-\sin(2x)\cdot\:2+\cos(2x)\cdot\:2)
tangent of-3x^2+6x+4	tangent\:-3x^{2}+6x+4
derivative of f(x)=2e^x+2/(\sqrt[3]{x)}	derivative\:f(x)=2e^{x}+\frac{2}{\sqrt[3]{x}}
sum from n=1 to infinity of n^5(1+n^6)^1	\sum\:_{n=1}^{\infty\:}n^{5}(1+n^{6})^{1}
integral of (z^3)/(\sqrt[3]{5+z^4)}	\int\:\frac{z^{3}}{\sqrt[3]{5+z^{4}}}dz
(dy)/(dx)=5-y	\frac{dy}{dx}=5-y
integral of e^{3x}cos(2x)	\int\:e^{3x}\cos(2x)dx
derivative of 5x^2cos(x)+4x	derivative\:5x^{2}\cos(x)+4x
y^{''}-2y^'-8y=0,y^'(0)=4,y(0)=-2	y^{\prime\:\prime\:}-2y^{\prime\:}-8y=0,y^{\prime\:}(0)=4,y(0)=-2
integral of sin(pi)x	\int\:\sin(π)xdx
tangent of f(x)=x^2+2,(1,3)	tangent\:f(x)=x^{2}+2,(1,3)
sum from n=1 to infinity of (15/4)^{n+1}	\sum\:_{n=1}^{\infty\:}(\frac{15}{4})^{n+1}
(\partial)/(\partial x)(x^{y^3})	\frac{\partial\:}{\partial\:x}(x^{y^{3}})
derivative of 9sqrt(x)-7/x	derivative\:9\sqrt{x}-\frac{7}{x}
limit as x approaches-9 of 1/((x+9)^2)	\lim\:_{x\to\:-9}(\frac{1}{(x+9)^{2}})
integral of cos^3(3x)sin^{-2}(3x)	\int\:\cos^{3}(3x)\sin^{-2}(3x)dx
limit as x approaches-infinity of 19	\lim\:_{x\to\:-\infty\:}(19)
limit as x approaches 5 of 9	\lim\:_{x\to\:5}(9)
tangent of f(x)=x-x^2,\at x=-1	tangent\:f(x)=x-x^{2},\at\:x=-1
derivative of f(x)=3x^5	derivative\:f(x)=3x^{5}
integral of ((8x-5)/(\sqrt[3]{x)})	\int\:(\frac{8x-5}{\sqrt[3]{x}})dx
integral of sqrt(1+x^2)2x	\int\:\sqrt{1+x^{2}}2xdx
inverse oflaplace 1/((s+20)[(s+2)^2+1])	inverselaplace\:\frac{1}{(s+20)[(s+2)^{2}+1]}
sum from n=0 to infinity of (3^n)/(1000)	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{1000}
(dy)/(dx)=x^2y	\frac{dy}{dx}=x^{2}y
derivative of (4x-4sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{4x-4\sqrt{1+x}}{x^{2}-1})
tangent of y=6cos(x)+3sin(2x)	tangent\:y=6\cos(x)+3\sin(2x)
derivative of (8x^2+8x+2/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+8x+2}{\sqrt{x}})
integral of (sqrt(x))/1	\int\:\frac{\sqrt{x}}{1}dx
area x=5y^2,x=1+4y^2	area\:x=5y^{2},x=1+4y^{2}
derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4	derivative\:3x^{-\frac{3}{2}}+6x^{-\frac{1}{2}}+x^{3}-4
derivative of y=e^{3sqrt(x)}	derivative\:y=e^{3\sqrt{x}}
derivative of (x^2+1e^x)	\frac{d}{dx}((x^{2}+1)e^{x})
derivative of 2sqrt(3x)	derivative\:2\sqrt{3x}
integral of xsqrt(16-x^2)	\int\:x\sqrt{16-x^{2}}dx
d/(ds)((s^2-4s+20)/(s^2+6s+8))	\frac{d}{ds}(\frac{s^{2}-4s+20}{s^{2}+6s+8})
derivative of (x-3^3+3(x-3)^2+6)	\frac{d}{dx}((x-3)^{3}+3(x-3)^{2}+6)
integral of (4x^4+x+1)/(x^5+x^4)	\int\:\frac{4x^{4}+x+1}{x^{5}+x^{4}}dx
derivative of ln(225sin^2(x))	derivative\:\ln(225\sin^{2}(x))
tangent of y= 1/(sqrt(x))	tangent\:y=\frac{1}{\sqrt{x}}
integral from 1 to infinity of x^{-3}	\int\:_{1}^{\infty\:}x^{-3}dx
y^'-5y=4e^{7t}	y^{\prime\:}-5y=4e^{7t}
limit as x approaches 0 of x^2+ax+2	\lim\:_{x\to\:0}(x^{2}+ax+2)
laplacetransform 2t^2-3t-1	laplacetransform\:2t^{2}-3t-1
integral of 1/(sqrt(4x^2-81))	\int\:\frac{1}{\sqrt{4x^{2}-81}}dx
integral of (x^3)/(sqrt(25+x^8))	\int\:\frac{x^{3}}{\sqrt{25+x^{8}}}dx
derivative of 3+vt-4.9t^2	derivative\:3+vt-4.9t^{2}
integral from 0 to 5 of 1/(sqrt(25-x^2))	\int\:_{0}^{5}\frac{1}{\sqrt{25-x^{2}}}dx
(\partial)/(\partial y)((x^2)/(y^3))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}}{y^{3}})
(\partial)/(\partial θ)(r(θ)cos^2(θ))	\frac{\partial\:}{\partial\:θ}(r(θ)\cos^{2}(θ))
derivative of 4x^2-sin(x)	\frac{d}{dx}(4x^{2}-\sin(x))
derivative of Axe^{-3x}	\frac{d}{dx}(Axe^{-3x})
integral of (csc(θ)cot(θ))/(5-4csc(θ))	\int\:\frac{\csc(θ)\cot(θ)}{5-4\csc(θ)}dθ
f(x)=e^{6x}	f(x)=e^{6x}
(x+2)dt=2t+3dx	(x+2)dt=2t+3dx
(\partial}{\partial x}(\frac{x^2)/4)	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{4})
(\partial)/(\partial x)(x^6y^4-x^5y^3)	\frac{\partial\:}{\partial\:x}(x^{6}y^{4}-x^{5}y^{3})
integral of (1/(sqrt(x^2-4)))	\int\:(\frac{1}{\sqrt{x^{2}-4}})dx
slope of (0,-3),(-4,2)	slope\:(0,-3),(-4,2)
inverse oflaplace s^3	inverselaplace\:s^{3}
integral of+(sin(x))/(cos(x)-cos^2(x))	\int\:+\frac{\sin(x)}{\cos(x)-\cos^{2}(x)}dx
integral of y/(sqrt(y+1)-(y+1))	\int\:\frac{y}{\sqrt{y+1}-(y+1)}dy
integral of 1/(e^x+e^{-x)}	\int\:\frac{1}{e^{x}+e^{-x}}dx
derivative of 1/(n+ke^n)	derivative\:\frac{1}{n+ke^{n}}
derivative of f(x)=3(x)^3+cos(x)	derivative\:f(x)=3(x)^{3}+\cos(x)

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