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Popular Calculus Problems

limit as x approaches 0 of (e^{\|x\|}-1)/x	\lim\:_{x\to\:0}(\frac{e^{\left\|x\right\|}-1}{x})
(dy}{dt}=\frac{4t)/k-0.1yt	\frac{dy}{dt}=\frac{4t}{k}-0.1yt
integral from 0 to pi of 8sin^4(x)	\int\:_{0}^{π}8\sin^{4}(x)dx
integral of ((2x+3))/(sqrt(x^2+3x))	\int\:\frac{(2x+3)}{\sqrt{x^{2}+3x}}dx
derivative of ln(sec(3x)+tan(3x))	derivative\:\ln(\sec(3x)+\tan(3x))
integral of 2e^{-2x}sin(x)	\int\:2e^{-2x}\sin(x)dx
(\partial)/(\partial y)(e^xln(y))	\frac{\partial\:}{\partial\:y}(e^{x}\ln(y))
d/(dy)(ysin(xy))	\frac{d}{dy}(y\sin(xy))
area x^2+4,-x^2-1,[0,1]	area\:x^{2}+4,-x^{2}-1,[0,1]
(dy)/(dx)=(2xy+2x)/(x^2+1)	\frac{dy}{dx}=\frac{2xy+2x}{x^{2}+1}
integral from 1 to infinity of 1/(x^8)	\int\:_{1}^{\infty\:}\frac{1}{x^{8}}dx
(\partial)/(\partial x)(4xy-3x^2)	\frac{\partial\:}{\partial\:x}(4xy-3x^{2})
y^'=2x,y(1)=7	y^{\prime\:}=2x,y(1)=7
xy^'=x^2sin(x)+y	xy^{\prime\:}=x^{2}\sin(x)+y
tangent of f(x)=(36x)/(x^2+36)	tangent\:f(x)=\frac{36x}{x^{2}+36}
integral of ((4x^2))/((x-2)(x^2+4))	\int\:\frac{(4x^{2})}{(x-2)(x^{2}+4)}dx
integral of (x^n)/n	\int\:\frac{x^{n}}{n}dx
integral from 5 to 9 of ((x-4)/(x^2))	\int\:_{5}^{9}(\frac{x-4}{x^{2}})dx
derivative of (x^2+4x+5x^3/(x+1))	\frac{d}{dx}(\frac{x^{2}+4x+5x^{3}}{x+1})
integral from 1 to 2 of 2^{-x}	\int\:_{1}^{2}2^{-x}dx
integral from 0 to 1 of (25)/(4y-1)	\int\:_{0}^{1}\frac{25}{4y-1}dy
limit as x approaches 0+of xln(x+x^2)	\lim\:_{x\to\:0+}(x\ln(x+x^{2}))
(dP)/(dx)=P-P^2	\frac{dP}{dx}=P-P^{2}
derivative of 3x-6	\frac{d}{dx}(3x-6)
integral of e^{sqrt(x)} 1/(sqrt(x))	\int\:e^{\sqrt{x}}\frac{1}{\sqrt{x}}dx
integral of 1/(sqrt(x+2)+x)	\int\:\frac{1}{\sqrt{x+2}+x}dx
integral of xsqrt(-x^2+3x-2)	\int\:x\sqrt{-x^{2}+3x-2}dx
d/(dt)(acos(4t)+bsin(4t))	\frac{d}{dt}(a\cos(4t)+b\sin(4t))
derivative of ln(2cos^4(θ))	derivative\:\ln(2\cos^{4}(θ))
(xe^x)^'	(xe^{x})^{\prime\:}
(dy)/(dx)=y^3xe^{x^2},y(0)=1	\frac{dy}{dx}=y^{3}xe^{x^{2}},y(0)=1
derivative of \sqrt[5]{2x}	derivative\:\sqrt[5]{2x}
limit as x approaches 3 of 4x^2-3x+2	\lim\:_{x\to\:3}(4x^{2}-3x+2)
integral of 1372x\sqrt[3]{7x+1}	\int\:1372x\sqrt[3]{7x+1}dx
integral of 1/(z^2+6z+10)	\int\:\frac{1}{z^{2}+6z+10}dz
derivative of 3x^2+7x-2	\frac{d}{dx}(3x^{2}+7x-2)
(dx)/(dy)=xsqrt(1-y^2)	\frac{dx}{dy}=x\sqrt{1-y^{2}}
derivative of x/3	derivative\:\frac{x}{3}
y^{''}-7y^'+10y=e^{3x}	y^{\prime\:\prime\:}-7y^{\prime\:}+10y=e^{3x}
(\partial)/(\partial x)(2zcos(x))	\frac{\partial\:}{\partial\:x}(2\cdot\:z\cdot\:\cos(x))
limit as x approaches 0 of (2ln(x+1))/x	\lim\:_{x\to\:0}(\frac{2\ln(x+1)}{x})
derivative of 3e^{-x^2}	derivative\:3e^{-x^{2}}
derivative of y=x^3sin^2(x)	derivative\:y=x^{3}\sin^{2}(x)
derivative of f(x)=e^{x^2-x}	derivative\:f(x)=e^{x^{2}-x}
tangent of sqrt(3x+1),\at a=8	tangent\:\sqrt{3x+1},\at\:a=8
integral of sin((1-x)/3)	\int\:\sin(\frac{1-x}{3})dx
factor cos^2(ln(e^{2x+1}(-2x)))	factor\:\cos^{2}(\ln(e^{2x+1}(-2x)))
inverse oflaplace (3e^{-pis})/(s^2+9)	inverselaplace\:\frac{3e^{-πs}}{s^{2}+9}
tangent of f(x)=4x^2-1,(-6,3)	tangent\:f(x)=4x^{2}-1,(-6,3)
y^'=(x+y-2)^2,y(0)=0	y^{\prime\:}=(x+y-2)^{2},y(0)=0
derivative of 2cos(pit)	derivative\:2\cos(πt)
(\partial)/(\partial y)((x-5)^{1/4}y^{1/4})	\frac{\partial\:}{\partial\:y}((x-5)^{\frac{1}{4}}y^{\frac{1}{4}})
derivative of x^{sqrt(x)+1}	\frac{d}{dx}(x^{\sqrt{x}+1})
derivative of-e^{-xy}	\frac{d}{dx}(-e^{-xy})
integral from 1 to infinity of (e^{-x})	\int\:_{1}^{\infty\:}(e^{-x})dx
integral of 6/(x-1)	\int\:\frac{6}{x-1}dx
integral of \sqrt[3]{(8-x)^4}	\int\:\sqrt[3]{(8-x)^{4}}dx
integral of sqrt(3x+2)	\int\:\sqrt{3x+2}dx
((x^2+3)dy)/(dx)=xy,y(1)=8	\frac{(x^{2}+3)dy}{dx}=xy,y(1)=8
derivative of 4ln(x)	derivative\:4\ln(x)
(\partial)/(\partial u)(usqrt(v-w))	\frac{\partial\:}{\partial\:u}(u\sqrt{v-w})
tangent of 2x^2+3x,\at x=1	tangent\:2x^{2}+3x,\at\:x=1
derivative of f(x)=5x-3	derivative\:f(x)=5x-3
sum from n=1 to infinity of n^{(-1/2)}	\sum\:_{n=1}^{\infty\:}n^{(-\frac{1}{2})}
derivative of 2x+3/x	derivative\:2x+\frac{3}{x}
(\partial)/(\partial x)(2x+5y+3)	\frac{\partial\:}{\partial\:x}(2x+5y+3)
(y+1)(dy)/(dx)=2x	(y+1)\frac{dy}{dx}=2x
area x^3,x^5	area\:x^{3},x^{5}
integral from 2 to 5 of (1-x^2)-(11-7x)	\int\:_{2}^{5}(1-x^{2})-(11-7x)dx
integral of 1/(x^{3/4)}	\int\:\frac{1}{x^{\frac{3}{4}}}dx
limit as x approaches 0 of 2^{1/2}	\lim\:_{x\to\:0}(2^{\frac{1}{2}})
integral from 5 to infinity of e^{-x/4}	\int\:_{5}^{\infty\:}e^{-\frac{x}{4}}dx
integral of 3/((x+1)^2)	\int\:\frac{3}{(x+1)^{2}}dx
integral of sqrt(1+9/4 x)	\int\:\sqrt{1+\frac{9}{4}x}dx
integral of 1+x^3	\int\:1+x^{3}dx
tangent of f(x)=(x^2)/(x-3)	tangent\:f(x)=\frac{x^{2}}{x-3}
derivative of e^{2x}cos(3x)	derivative\:e^{2x}\cos(3x)
tangent of f(x)=4tan(x),\at x= pi/3	tangent\:f(x)=4\tan(x),\at\:x=\frac{π}{3}
integral from 0 to 3 of pi(9-x^2)^2	\int\:_{0}^{3}π(9-x^{2})^{2}dx
limit as x approaches 0+of (x^3+3)/x	\lim\:_{x\to\:0+}(\frac{x^{3}+3}{x})
limit as x approaches 4 of 6-x	\lim\:_{x\to\:4}(6-x)
derivative of e^{3x}x	\frac{d}{dx}(e^{3x}x)
derivative of csc(x*cot(x))	\frac{d}{dx}(\csc(x)\cdot\:\cot(x))
integral of (Inx)/(sqrt(x))	\int\:\frac{Inx}{\sqrt{x}}dx
y^{'''}-y^{''}-8y^'+12y=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}-8y^{\prime\:}+12y=0
x(dy)/(dx)-2y=0	x\frac{dy}{dx}-2y=0
integral of 2x(x^2-9)^3	\int\:2x(x^{2}-9)^{3}dx
derivative of A*sin(kx-ωt)	\frac{d}{dx}(A\cdot\:\sin(kx-ωt))
integral from 2 to 3 of (21)/(sqrt(3-x))	\int\:_{2}^{3}\frac{21}{\sqrt{3-x}}dx
integral of cos(pit)	\int\:\cos(πt)dt
tangent of y=x(27x^{-2}+4)	tangent\:y=x(27x^{-2}+4)
limit as x approaches+2+of x/(x-2)	\lim\:_{x\to\:+2+}(\frac{x}{x-2})
integral of x*e^{-sx}	\int\:x\cdot\:e^{-sx}dx
(\partial)/(\partial y)((e^y)/(e^x+e^y))	\frac{\partial\:}{\partial\:y}(\frac{e^{y}}{e^{x}+e^{y}})
derivative of 3x^2-2x+5	\frac{d}{dx}(3x^{2}-2x+5)
integral of (xye^{xz})	\int\:(xye^{xz})dz
integral of sqrt(x)Inx	\int\:\sqrt{x}Inxdx
integral of-1/((x-1)^2)	\int\:-\frac{1}{(x-1)^{2}}dx
derivative of (3w^6-w)/w	derivative\:\frac{3w^{6}-w}{w}
(1/((4-x)^2))^'	(\frac{1}{(4-x)^{2}})^{\prime\:}

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