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Popular Calculus Problems

derivative of sqrt(2x-2)	\frac{d}{dx}(\sqrt{2x-2})
derivative of 3x^2-10x+7	\frac{d}{dx}(3x^{2}-10x+7)
integral from 0 to 1 of (1+sqrt(x))^8	\int\:_{0}^{1}(1+\sqrt{x})^{8}dx
(\partial)/(\partial x)(e^{3xyz-2})	\frac{\partial\:}{\partial\:x}(e^{3xyz-2})
derivative of (3x+1/(x^2+1))	\frac{d}{dx}(\frac{3x+1}{x^{2}+1})
limit as x approaches pi/2 of (sin(x))/x	\lim\:_{x\to\:\frac{π}{2}}(\frac{\sin(x)}{x})
area x=(y^2)/4 ,x= y/2+2	area\:x=\frac{y^{2}}{4},x=\frac{y}{2}+2
sum from n=0 to infinity of nsin(npi)	\sum\:_{n=0}^{\infty\:}n\sin(nπ)
integral of x/(x(x+4))	\int\:\frac{x}{x(x+4)}dx
(\partial)/(\partial x)(e^x*y)	\frac{\partial\:}{\partial\:x}(e^{x}\cdot\:y)
derivative of f(x)=sqrt(x)+7/(sqrt(x))	derivative\:f(x)=\sqrt{x}+\frac{7}{\sqrt{x}}
integral of x*ln(1+x)	\int\:x\cdot\:\ln(1+x)dx
area x^3-5x^2-x+5,1,5	area\:x^{3}-5x^{2}-x+5,1,5
integral of e^{-2x}sin(x/2)	\int\:e^{-2x}\sin(\frac{x}{2})dx
derivative of f(x)=arctan(2/x)	derivative\:f(x)=\arctan(\frac{2}{x})
integral of x*cos(kx)	\int\:x\cdot\:\cos(kx)dx
tangent of-10x^4+x^3	tangent\:-10x^{4}+x^{3}
derivative of y=x^{13/14}	derivative\:y=x^{\frac{13}{14}}
sum from n=1 to infinity of ln((n+1)^2)	\sum\:_{n=1}^{\infty\:}\ln((n+1)^{2})
2y^{''}+5y^'-3y=0,y(0)=1,y^'(0)=4	2y^{\prime\:\prime\:}+5y^{\prime\:}-3y=0,y(0)=1,y^{\prime\:}(0)=4
sum from n=0 to infinity of 1/(3^{n+1)}	\sum\:_{n=0}^{\infty\:}\frac{1}{3^{n+1}}
integral of tan^3(2t)sec^3(2t)	\int\:\tan^{3}(2t)\sec^{3}(2t)dt
(d^2)/(dx^2)(cos^2(2pix))	\frac{d^{2}}{dx^{2}}(\cos^{2}(2πx))
integral of sqrt(x^3)	\int\:\sqrt{x^{3}}dx
derivative of sqrt(ln(x^2+1))	derivative\:\sqrt{\ln(x^{2}+1)}
integral from-2 to 0 of sqrt(x/2+1)	\int\:_{-2}^{0}\sqrt{\frac{x}{2}+1}dx
y^'=(xe^y)/y	y^{\prime\:}=\frac{xe^{y}}{y}
t^2y^{''}-4ty^'+6y=0	t^{2}y^{\prime\:\prime\:}-4ty^{\prime\:}+6y=0
limit as x approaches 0 of (2x)/(2x^2)	\lim\:_{x\to\:0}(\frac{2x}{2x^{2}})
integral from 3 to 5 of e^{6x}	\int\:_{3}^{5}e^{6x}dx
derivative of f(x)=sqrt(3-2x)	derivative\:f(x)=\sqrt{3-2x}
integral of (x^4+1)/(x^2+1)	\int\:\frac{x^{4}+1}{x^{2}+1}dx
derivative of 0.882a^{0.842}	derivative\:0.882a^{0.842}
integral from-2 to 2 of \|x\|-(x^2-2)	\int\:_{-2}^{2}\left\|x\right\|-(x^{2}-2)dx
derivative of (x^3+1)e^x	derivative\:(x^{3}+1)e^{x}
integral of (x-2)^4 1/(sqrt(4x-x^2))	\int\:(x-2)^{4}\frac{1}{\sqrt{4x-x^{2}}}dx
integral of (x^2+7)e^{-x}	\int\:(x^{2}+7)e^{-x}dx
(\partial)/(\partial y)(3xz^3e^{y^2})	\frac{\partial\:}{\partial\:y}(3xz^{3}e^{y^{2}})
limit as x approaches 2 of 4x^2+x+4	\lim\:_{x\to\:2}(4x^{2}+x+4)
integral from 0 to pi/6 of (6sec^2(x))	\int\:_{0}^{\frac{π}{6}}(6\sec^{2}(x))dx
2y^{''}+4y^'-7y=7cos(2x)	2y^{\prime\:\prime\:}+4y^{\prime\:}-7y=7\cos(2x)
integral of sqrt(1+x)	\int\:\sqrt{1+x}dx
tangent of f(x)=e^{3x},\at x= 1/3 ln(5)	tangent\:f(x)=e^{3x},\at\:x=\frac{1}{3}\ln(5)
derivative of sin(xln(2x))	\frac{d}{dx}(\sin(x)\ln(2x))
derivative of x*e^{-3x}	\frac{d}{dx}(x\cdot\:e^{-3x})
integral of (cos(θ))/(1+sin^2(θ))	\int\:\frac{\cos(θ)}{1+\sin^{2}(θ)}dθ
integral of (1+ye^{xy})	\int\:(1+ye^{xy})dx
integral of 1/(x(ln(x))^2)	\int\:\frac{1}{x(\ln(x))^{2}}dx
derivative of (e^x/(x^2+1))	\frac{d}{dx}(\frac{e^{x}}{x^{2}+1})
integral of 18x	\int\:18xdx
implicit (dy)/(dx),8x^3+x^2y-xy^3=9	implicit\:\frac{dy}{dx},8x^{3}+x^{2}y-xy^{3}=9
integral of 1/(x^{4/5)(1+x^{1/5})}	\int\:\frac{1}{x^{\frac{4}{5}}(1+x^{\frac{1}{5}})}dx
x((dy)/(dx))=2x^2+y	x(\frac{dy}{dx})=2x^{2}+y
tangent of f(x)=sqrt(7x+32),\at x=-1	tangent\:f(x)=\sqrt{7x+32},\at\:x=-1
(x+y)dx+(x+y-1)dy=0	(x+y)dx+(x+y-1)dy=0
integral of ((-y)/(x^2+y^2))	\int\:(\frac{-y}{x^{2}+y^{2}})dx
(\partial)/(\partial x)((x-y)sin(3x+2y))	\frac{\partial\:}{\partial\:x}((x-y)\sin(3x+2y))
inverse oflaplace 6/((s^2(s^2+8s+1)))	inverselaplace\:\frac{6}{(s^{2}(s^{2}+8s+1))}
derivative of y=ln\|x\|	derivative\:y=\ln\left\|x\right\|
tangent of f(x)=sqrt(x-8),\at x=12	tangent\:f(x)=\sqrt{x-8},\at\:x=12
integral of x^2+4e^x+C	\int\:x^{2}+4e^{x}+Cdx
(\partial)/(\partial x)(2x^3y^2)	\frac{\partial\:}{\partial\:x}(2\cdot\:x^{3}\cdot\:y^{2})
integral from 0 to 1 of cos(npix)	\int\:_{0}^{1}\cos(nπx)dx
derivative of ln(6x^4-9x-3)	\frac{d}{dx}(\ln(6x^{4}-9x-3))
y^{''}+8y=0	y^{\prime\:\prime\:}+8y=0
derivative of arctan(9^x)	\frac{d}{dx}(\arctan(9^{x}))
(dx)/(dt)+2tx^3+x/t =0	\frac{dx}{dt}+2tx^{3}+\frac{x}{t}=0
(\partial)/(\partial x)(3-(x^2+y^2)^{1/3})	\frac{\partial\:}{\partial\:x}(3-(x^{2}+y^{2})^{\frac{1}{3}})
integral of 7e^{-0.4x}	\int\:7e^{-0.4x}dx
(2y+1)=(dy)/(dt)	(2y+1)=\frac{dy}{dt}
derivative of f(x)=4x^{-2}	derivative\:f(x)=4x^{-2}
integral of 6t^2\sqrt[3]{t}	\int\:6t^{2}\sqrt[3]{t}dt
integral of sqrt(3/4-x^2)	\int\:\sqrt{\frac{3}{4}-x^{2}}dx
derivative of x^2+7x	\frac{d}{dx}(x^{2}+7x)
integral of (2x+2)/(x^2+1)	\int\:\frac{2x+2}{x^{2}+1}dx
integral of (x^7e^x-8x^6)/(x^7)	\int\:\frac{x^{7}e^{x}-8x^{6}}{x^{7}}dx
derivative of log_{18}(x^2-5x)	\frac{d}{dx}(\log_{18}(x^{2}-5x))
taylor x/(e^x-1)	taylor\:\frac{x}{e^{x}-1}
derivative of 2ln(x^2)	\frac{d}{dx}(2\ln(x^{2}))
sum from n=1 to infinity of 10^nx^n	\sum\:_{n=1}^{\infty\:}10^{n}x^{n}
integral of (x^2+5x+6)cos(2x)	\int\:(x^{2}+5x+6)\cos(2x)dx
area y=x,g(y,x)=x^2,[0,1]	area\:y=x,g(y,x)=x^{2},[0,1]
derivative of cos(sin^3(5x-5))	\frac{d}{dx}(\cos(\sin^{3}(5x-5)))
y^'=((y^3+1))/((3xy^2))	y^{\prime\:}=\frac{(y^{3}+1)}{(3xy^{2})}
limit as x approaches+1 of (1-\|x\|)/(x-1)	\lim\:_{x\to\:+1}(\frac{1-\left\|x\right\|}{x-1})
integral of (x^3)/(sqrt(1+x^4))	\int\:\frac{x^{3}}{\sqrt{1+x^{4}}}dx
y^'-y+x^2=0	y^{\prime\:}-y+x^{2}=0
integral from 3 to 6 of 1/(x^2-1)	\int\:_{3}^{6}\frac{1}{x^{2}-1}dx
integral of x^{2/9}	\int\:x^{\frac{2}{9}}dx
(\partial)/(\partial y)(ln(x+8y+5z))	\frac{\partial\:}{\partial\:y}(\ln(x+8y+5z))
(dy)/(dx)-2xy=-6x^2e^{x^2}	\frac{dy}{dx}-2xy=-6x^{2}e^{x^{2}}
limit as x approaches 0 of (sin(c)x)/x	\lim\:_{x\to\:0}(\frac{\sin(c)x}{x})
limit as x approaches 0+of x^{x^3}	\lim\:_{x\to\:0+}(x^{x^{3}})
sum from n=1 to infinity of ((1)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(1)^{n}}{n}
sum from n=0 to infinity of 17/2	\sum\:_{n=0}^{\infty\:}\frac{17}{2}
(\partial)/(\partial y)(e^{xyz^2}yz^2)	\frac{\partial\:}{\partial\:y}(e^{xyz^{2}}yz^{2})
derivative of (2x+1^4+8x(2x+1)^3)	\frac{d}{dx}((2x+1)^{4}+8x(2x+1)^{3})
integral of (28e^{4x})/(sqrt(6+e^{4x))}	\int\:\frac{28e^{4x}}{\sqrt{6+e^{4x}}}dx
laplacetransform te^{10t}	laplacetransform\:te^{10t}
limit as x approaches 0 of ((arctan(4x)))/(ln(x))	\lim\:_{x\to\:0}(\frac{(\arctan(4x))}{\ln(x)})

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