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Popular Calculus Problems

integral of e^{10t}	\int\:e^{10t}dt
derivative of f(x^{-1}(x))	\frac{d}{dx}(f(x)^{-1}(x))
x^2y^'+2xy=21cos^2(x)	x^{2}y^{\prime\:}+2xy=21\cos^{2}(x)
derivative of (sqrt(x))/(x-1)	derivative\:\frac{\sqrt{x}}{x-1}
derivative of sqrt(x)^{9x}	\frac{d}{dx}(\sqrt{x}^{9x})
integral from 0 to 1 of (x^2-8)e^{-x}	\int\:_{0}^{1}(x^{2}-8)e^{-x}dx
(x^2-y^2)(dy)/(dx)=2xy	(x^{2}-y^{2})\frac{dy}{dx}=2xy
x^2yy^'=(y^2-1)^{3/2}	x^{2}yy^{\prime\:}=(y^{2}-1)^{\frac{3}{2}}
derivative of xln(1/x)	\frac{d}{dx}(x\ln(\frac{1}{x}))
derivative of y=2	derivative\:y=2
(dx)/(dt)=tx^{1/3},x(1)=1	\frac{dx}{dt}=tx^{\frac{1}{3}},x(1)=1
integral from 0 to 4 of x/(sqrt(9+x^2))	\int\:_{0}^{4}\frac{x}{\sqrt{9+x^{2}}}dx
derivative of 10x^2e^x	\frac{d}{dx}(10x^{2}e^{x})
derivative of (x^3)/3+(x^2)/2+x	derivative\:\frac{x^{3}}{3}+\frac{x^{2}}{2}+x
(dy)/(dx)=(y+5)(x+2)	\frac{dy}{dx}=(y+5)(x+2)
derivative of-x/(10)	\frac{d}{dx}(-\frac{x}{10})
integral of 2xln(5x)	\int\:2x\ln(5x)dx
(dy)/(dx)=x^4y	\frac{dy}{dx}=x^{4}y
integral of 7x-4	\int\:7x-4dx
integral of 1/((y+4)^2)	\int\:\frac{1}{(y+4)^{2}}dy
limit as x approaches infinity of 4x+1	\lim\:_{x\to\:\infty\:}(4x+1)
derivative of 3-x^2	derivative\:3-x^{2}
tangent of y=2x^2-13x+3	tangent\:y=2x^{2}-13x+3
integral of x^22^{x^3+1}	\int\:x^{2}2^{x^{3}+1}dx
integral of u^{-2}	\int\:u^{-2}du
integral of (x^2+4)^72x	\int\:(x^{2}+4)^{7}2xdx
derivative of sin(pix+1)	\frac{d}{dx}(\sin(πx+1))
derivative of tan(x^3+3)	\frac{d}{dx}(\tan(x^{3}+3))
integral from 0 to 4 of (x+1)^2	\int\:_{0}^{4}(x+1)^{2}dx
integral from 0 to infinity of sin(3x)	\int\:_{0}^{\infty\:}\sin(3x)dx
derivative of f(x)=-4x^2+3x	derivative\:f(x)=-4x^{2}+3x
(\partial)/(\partial x)(e^y-sin(x))	\frac{\partial\:}{\partial\:x}(e^{y}-\sin(x))
integral from 0 to 2pi of integral of 1	\int\:_{0}^{2π}\int\:1dxdy
(\partial)/(\partial z)(z^3)	\frac{\partial\:}{\partial\:z}(z^{3})
limit as x approaches-9 of 5x	\lim\:_{x\to\:-9}(5x)
limit as x approaches 0 of (-1)/(x^2)	\lim\:_{x\to\:0}(\frac{-1}{x^{2}})
(\partial)/(\partial x)(4x^2y+2xy^2)	\frac{\partial\:}{\partial\:x}(4x^{2}y+2xy^{2})
derivative of sin(cos(x))	derivative\:\sin(\cos(x))
integral of 1/(3sqrt(x)(4+\sqrt{x))}	\int\:\frac{1}{3\sqrt{x}(4+\sqrt{x})}dx
integral of-3x^2e^x	\int\:-3x^{2}e^{x}dx
derivative of 7(\sqrt[3]{x}+(x^{1/3}/3))	\frac{d}{dx}(7(\sqrt[3]{x}+\frac{x^{\frac{1}{3}}}{3}))
(\partial)/(\partial x)(x+3log_{10}(x)-y^2)	\frac{\partial\:}{\partial\:x}(x+3\log_{10}(x)-y^{2})
integral of (18)/(xsqrt(1+2x))	\int\:\frac{18}{x\sqrt{1+2x}}dx
limit as x approaches 1+of (x+1)/(x-1)	\lim\:_{x\to\:1+}(\frac{x+1}{x-1})
y^{''}-5y^'+4y=0	y^{\prime\:\prime\:}-5y^{\prime\:}+4y=0
integral of (6x)/(x^2+1)	\int\:\frac{6x}{x^{2}+1}dx
(d^2)/(dx^2)((6x^2+8)^6)	\frac{d^{2}}{dx^{2}}((6x^{2}+8)^{6})
sum from n=1 to infinity of 4/(pi^n)	\sum\:_{n=1}^{\infty\:}\frac{4}{π^{n}}
integral of x^2sqrt(6x+3)	\int\:x^{2}\sqrt{6x+3}dx
derivative of f(x)= 1/(5x+7)	derivative\:f(x)=\frac{1}{5x+7}
taylor 1/((1+x))	taylor\:\frac{1}{(1+x)}
y^{''}+5y^'+6=0	y^{\prime\:\prime\:}+5y^{\prime\:}+6=0
tangent of y=sin(sin(x)),(4pi,0)	tangent\:y=\sin(\sin(x)),(4π,0)
derivative of 3x^2-15	\frac{d}{dx}(3x^{2}-15)
sum from n=1 to infinity of n/(n+6)	\sum\:_{n=1}^{\infty\:}\frac{n}{n+6}
limit as x approaches 0 of (1-6x)^{2/x}	\lim\:_{x\to\:0}((1-6x)^{\frac{2}{x}})
integral of 1/(x^{11)}	\int\:\frac{1}{x^{11}}dx
xy^2(x(dy)/(dx)+y)=9	xy^{2}(x\frac{dy}{dx}+y)=9
limit as x approaches 5+of ln(x-5)	\lim\:_{x\to\:5+}(\ln(x-5))
derivative of (2^x/(3x-1))	\frac{d}{dx}(\frac{2^{x}}{3x-1})
integral of (4x+7)/((3x+2)(x-5))	\int\:\frac{4x+7}{(3x+2)(x-5)}dx
integral of x^2ln(8x)	\int\:x^{2}\ln(8x)dx
derivative of 6-2x	\frac{d}{dx}(6-2x)
integral of sin^3(θ)	\int\:\sin^{3}(θ)dθ
integral of \sqrt[3]{e^x}	\int\:\sqrt[3]{e^{x}}dx
(\partial}{\partial u}(\frac{u+v)/3)	\frac{\partial\:}{\partial\:u}(\frac{u+v}{3})
49y^{''}+126y^'+81y=0	49y^{\prime\:\prime\:}+126y^{\prime\:}+81y=0
integral from 0 to pi/3 of tan^3(x)	\int\:_{0}^{\frac{π}{3}}\tan^{3}(x)dx
integral of cos^3(x/(19))	\int\:\cos^{3}(\frac{x}{19})dx
integral of (cos(x))^3	\int\:(\cos(x))^{3}dx
(\partial)/(\partial y)(arctan(x+2y))	\frac{\partial\:}{\partial\:y}(\arctan(x+2y))
integral of (5-5x)/(1-sqrt(x))	\int\:\frac{5-5x}{1-\sqrt{x}}dx
x^{''}+8x^'+16x=0	x^{\prime\:\prime\:}+8x^{\prime\:}+16x=0
derivative of sqrt(5x-8)	\frac{d}{dx}(\sqrt{5x-8})
taylor X^{9/6},7	taylor\:X^{\frac{9}{6}},7
derivative of tan(3^x)	\frac{d}{dx}(\tan(3^{x}))
(\partial)/(\partial x)(2/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{2}{x+y})
derivative of sqrt(x/(x+9))	derivative\:\sqrt{\frac{x}{x+9}}
derivative of 1/((1-x^2))	\frac{d}{dx}(\frac{1}{(1-x)^{2}})
integral from 0 to 1 of x/((x+1)(x^2+1))	\int\:_{0}^{1}\frac{x}{(x+1)(x^{2}+1)}dx
integral from 0 to 1 of arctan(2x)	\int\:_{0}^{1}\arctan(2x)dx
integral of x(x-5)^2	\int\:x(x-5)^{2}dx
derivative of 3/(6x^{-2})	\frac{d}{dx}(\frac{3}{6x^{-2}})
derivative of f(x)=(x^3)/(24)+2/x	derivative\:f(x)=\frac{x^{3}}{24}+\frac{2}{x}
integral from 1 to 2 of 1/(sqrt(4-t^2))	\int\:_{1}^{2}\frac{1}{\sqrt{4-t^{2}}}dt
tangent of-3x^2+2xy+2y^3=125,(3,4)	tangent\:-3x^{2}+2xy+2y^{3}=125,(3,4)
derivative of y=ln(10x^2-8)	\frac{d}{dx}y=\ln(10x^{2}-8)
tangent of x^3-3x^2+2x-2	tangent\:x^{3}-3x^{2}+2x-2
derivative of Inx	\frac{d}{dx}(Inx)
tangent of f(x)=x^3-2x^2+1,\at x=1	tangent\:f(x)=x^{3}-2x^{2}+1,\at\:x=1
derivative of arcsin(e^{2x})	\frac{d}{dx}(\arcsin(e^{2x}))
integral of (x^4)/5	\int\:\frac{x^{4}}{5}dx
derivative of 4x^2*sin(4x)	\frac{d}{dx}(4x^{2}\cdot\:\sin(4x))
integral of x(x+2)^6	\int\:x(x+2)^{6}dx
integral from-x to x^2 of e^{t^2}	\int\:_{-x}^{x^{2}}e^{t^{2}}dt
integral of sqrt(7x+2)	\int\:\sqrt{7x+2}dx
inverse oflaplace (5se^{-s})/(2s^2+32)	inverselaplace\:\frac{5se^{-s}}{2s^{2}+32}
integral of (x+1)/((x+2)^3)	\int\:\frac{x+1}{(x+2)^{3}}dx
9y^{''}-12y^'+4y=e^{-3x}	9y^{\prime\:\prime\:}-12y^{\prime\:}+4y=e^{-3x}
integral of (e^x)/(e^x+e^{2x)-2}	\int\:\frac{e^{x}}{e^{x}+e^{2x}-2}dx

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