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Popular Calculus Problems

integral of (ln(x))/(xsqrt(1+ln(x)))	\int\:\frac{\ln(x)}{x\sqrt{1+\ln(x)}}dx
longdivision ((x+1))/((x-1))	longdivision\:\frac{(x+1)}{(x-1)}
tangent of f(x)=x^2+3,(-1,4)	tangent\:f(x)=x^{2}+3,(-1,4)
integral from 2 to t of 1/(5x^2)	\int\:_{2}^{t}\frac{1}{5x^{2}}dx
derivative of (x+2^2-3x)	\frac{d}{dx}((x+2)^{2}-3x)
integral of (8x^2-7x+16)/(x^3+4x)	\int\:\frac{8x^{2}-7x+16}{x^{3}+4x}dx
integral from 1 to 3 of 1/(x^3)	\int\:_{1}^{3}\frac{1}{x^{3}}dx
derivative of xsqrt(3-x^2)	derivative\:x\sqrt{3-x^{2}}
limit as x approaches 2 of 1/(\|2-x\|)	\lim\:_{x\to\:2}(\frac{1}{\left\|2-x\right\|})
area y=-x^2+8x-12,y=x^2-8x+18,x=3x=6	area\:y=-x^{2}+8x-12,y=x^{2}-8x+18,x=3x=6
tangent of f(x)=6x^2+4x-7,-3	tangent\:f(x)=6x^{2}+4x-7,-3
integral of ((arcsin(x/3))^2)/(sqrt(9-x^2))	\int\:\frac{(\arcsin(\frac{x}{3}))^{2}}{\sqrt{9-x^{2}}}dx
(\partial)/(\partial y)((x-y)^5)	\frac{\partial\:}{\partial\:y}((x-y)^{5})
derivative of (5^x/(ln(5)))	\frac{d}{dx}(\frac{5^{x}}{\ln(5)})
integral of (e-x-e^2)(ex+e-5)	\int\:(e-x-e^{2})(ex+e-5)dx
integral of 3e^{3x}	\int\:3e^{3x}dx
derivative of 3/(x+3)	\frac{d}{dx}(\frac{3}{x+3})
2x-3ysqrt(x^2+1)(dy)/(dx)=0	2x-3y\sqrt{x^{2}+1}\frac{dy}{dx}=0
integral of sinh(ln(x))	\int\:\sinh(\ln(x))dx
integral of 4cos^3(3x)	\int\:4\cos^{3}(3x)dx
derivative of sqrt(sin(e^{x^4sin(x))})	\frac{d}{dx}(\sqrt{\sin(e^{x^{4}\sin(x)})})
derivative of ((2x^2/(4-x))^3)	\frac{d}{dx}((\frac{2x^{2}}{4-x})^{3})
integral of 3/(x^2+4x-5)	\int\:\frac{3}{x^{2}+4x-5}dx
limit as x approaches 0+of (1+x)^{2/x}	\lim\:_{x\to\:0+}((1+x)^{\frac{2}{x}})
derivative of f(x)=e^{x^5+2x}	derivative\:f(x)=e^{x^{5}+2x}
derivative of y=x^2y^3+x^3y^2	derivative\:y=x^{2}y^{3}+x^{3}y^{2}
(dy)/(dx)=e^{(6x-3y)}	\frac{dy}{dx}=e^{(6x-3y)}
derivative of 1/((16-x^2))	\frac{d}{dx}(\frac{1}{(16-x^{2})})
integral of 10sqrt(1+cos(4x))	\int\:10\sqrt{1+\cos(4x)}dx
derivative of ((x-1(x^2+4))/(x(x+1)))	\frac{d}{dx}(\frac{(x-1)(x^{2}+4)}{x(x+1)})
derivative of (100p)/(0.1p+1)	derivative\:\frac{100p}{0.1p+1}
integral of 6xy^3	\int\:6xy^{3}dx
implicit (dy)/(dx),3x^3+9xy^2=5x^3	implicit\:\frac{dy}{dx},3x^{3}+9xy^{2}=5x^{3}
derivative of (x^2+3x+2/(x+1))	\frac{d}{dx}(\frac{x^{2}+3x+2}{x+1})
inverse oflaplace 9/((s-2)(s-3))	inverselaplace\:\frac{9}{(s-2)(s-3)}
derivative of f(x)=(2x)(4x^2+6x^7+8)	derivative\:f(x)=(2x)(4x^{2}+6x^{7}+8)
integral of 1/(sqrt(b^2+a^2x^2))	\int\:\frac{1}{\sqrt{b^{2}+a^{2}x^{2}}}dx
integral of x^2ln(x)+e^{2x}+1	\int\:x^{2}\ln(x)+e^{2x}+1dx
derivative of x^2-1/x	\frac{d}{dx}(x^{2}-\frac{1}{x})
derivative of e^{-5x}	derivative\:e^{-5x}
derivative of x^2y^4e^y	\frac{d}{dx}(x^{2}y^{4}e^{y})
derivative of (x^2/(x^2-6))	\frac{d}{dx}(\frac{x^{2}}{x^{2}-6})
area 6-x^2,x^2-20<x<3	area\:6-x^{2},x^{2}-20<x<3
derivative of sqrt(4x-20)	derivative\:\sqrt{4x-20}
limit as x approaches infinity of x^4e^x	\lim\:_{x\to\:\infty\:}(x^{4}e^{x})
taylor ln(5-x)	taylor\:\ln(5-x)
y^{''}+484y=sec(22x)	y^{\prime\:\prime\:}+484y=\sec(22x)
limit as x approaches infinity of 7+9/x	\lim\:_{x\to\:\infty\:}(7+\frac{9}{x})
(\partial)/(\partial y)(sin(xyz))	\frac{\partial\:}{\partial\:y}(\sin(xyz))
derivative of 4/(5x)	\frac{d}{dx}(\frac{4}{5x})
(dy)/(dx)+3x^2y=0	\frac{dy}{dx}+3x^{2}y=0
d/(dy)(y/(x^2+y^2+1))	\frac{d}{dy}(\frac{y}{x^{2}+y^{2}+1})
integral from 0 to 1 of 2pix(18-18x)	\int\:_{0}^{1}2πx(18-18x)dx
integral of sin^2(x)cos(x)ln(sin(x))	\int\:\sin^{2}(x)\cos(x)\ln(\sin(x))dx
integral of sin^5(x)*cos^2(x)	\int\:\sin^{5}(x)\cdot\:\cos^{2}(x)dx
derivative of x^3-2x+1	\frac{d}{dx}(x^{3}-2x+1)
(\partial)/(\partial x)(2tan(xy))	\frac{\partial\:}{\partial\:x}(2\tan(xy))
y^'+ay=0	y^{\prime\:}+ay=0
derivative of 3x^e	\frac{d}{dx}(3x^{e})
sum from n=1 to infinity of ((1))/(n!)	\sum\:_{n=1}^{\infty\:}\frac{(1)}{n!}
area 3sqrt(x),3x	area\:3\sqrt{x},3x
y^'-6y+1=0	y^{\prime\:}-6y+1=0
y^{''}+y=te^t	y^{\prime\:\prime\:}+y=te^{t}
d/(d{x)}(sqrt({x){y}{z}})	\frac{d}{d{x}}(\sqrt{{x}{y}{z}})
integral from 1/2 to 1 of (x^{-3}-12)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-12)dx
limit as x approaches 1+of 2/(x-1)	\lim\:_{x\to\:1+}(\frac{2}{x-1})
derivative of f(x)=(x^2)/4	derivative\:f(x)=\frac{x^{2}}{4}
derivative of x^2+x-2	\frac{d}{dx}(x^{2}+x-2)
limit as x approaches 5 of x/0	\lim\:_{x\to\:5}(\frac{x}{0})
derivative of cos(xx^2)	\frac{d}{dx}(\cos(x)x^{2})
integral of 1/(x^2-4x+6)	\int\:\frac{1}{x^{2}-4x+6}dx
implicit (dy)/(dx),x^2+y^2=(2x^2+4y^2-x)2	implicit\:\frac{dy}{dx},x^{2}+y^{2}=(2x^{2}+4y^{2}-x)2
(dy)/(dx)=2(2x+y)^2	\frac{dy}{dx}=2(2x+y)^{2}
integral of 2cos(2x-5)	\int\:2\cos(2x-5)dx
limit as x approaches 42 of (x^2)/7-6/x	\lim\:_{x\to\:42}(\frac{x^{2}}{7}-\frac{6}{x})
derivative of (ln(2x)^3)	\frac{d}{dx}((\ln(2x))^{3})
integral from 0 to 7/6 of 7x-6x^2	\int\:_{0}^{\frac{7}{6}}7x-6x^{2}dx
derivative of 2/(sqrt(4+9x^4))	\frac{d}{dx}(\frac{2}{\sqrt{4+9x^{4}}})
(\partial)/(\partial y)(xsin(x+y))	\frac{\partial\:}{\partial\:y}(x\sin(x+y))
derivative of ln(6)x^3	derivative\:\ln(6)x^{3}
integral of 3x^2-2	\int\:3x^{2}-2dx
tangent of x^2+y^2=100,(6,8)	tangent\:x^{2}+y^{2}=100,(6,8)
tangent of y=x^2,(-0.6,0.36)	tangent\:y=x^{2},(-0.6,0.36)
integral of-ln\|cos(x)\|	\int\:-\ln\left\|\cos(x)\right\|dx
derivative of \sqrt[3]{1/x}	\frac{d}{dx}(\sqrt[3]{\frac{1}{x}})
integral of cos(20x)cos(13x)	\int\:\cos(20x)\cos(13x)dx
derivative of y=-1.97x^2+0.51x+8.1	derivative\:y=-1.97x^{2}+0.51x+8.1
integral of sin(26x)cos(17x)	\int\:\sin(26x)\cos(17x)dx
integral of xsin(kx)	\int\:x\sin(kx)dx
derivative of 2xe^{x^2}	derivative\:2xe^{x^{2}}
(\partial)/(\partial x)(nani)	\frac{\partial\:}{\partial\:x}(nani)
implicit (dy)/(dx),y= 9/x	implicit\:\frac{dy}{dx},y=\frac{9}{x}
limit as x approaches-1 of 1/(x^2+2x+1)	\lim\:_{x\to\:-1}(\frac{1}{x^{2}+2x+1})
derivative of 4^{sin(x)}	derivative\:4^{\sin(x)}
sin(2x)dx+cos(7y)dy=0,y(pi^2)=pi^7	\sin(2x)dx+\cos(7y)dy=0,y(π^{2})=π^{7}
derivative of sqrt(x/5)	\frac{d}{dx}(\sqrt{\frac{x}{5}})
(\partial)/(\partial x)(sqrt(y-x))	\frac{\partial\:}{\partial\:x}(\sqrt{y-x})
y^{''}+16y=8sin(4x)	y^{\prime\:\prime\:}+16y=8\sin(4x)
limit as x approaches 0 of x/(tan(3x))	\lim\:_{x\to\:0}(\frac{x}{\tan(3x)})
integral of 8tan^3(x)	\int\:8\tan^{3}(x)dx

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