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Popular Calculus Problems

integral of 1/(x(ln(x))^3)	\int\:\frac{1}{x(\ln(x))^{3}}dx
y^'=y(y+1)x	y^{\prime\:}=y(y+1)x
integral of (1+ln(x))/(xln(x))	\int\:\frac{1+\ln(x)}{x\ln(x)}dx
derivative of 3sin^2(xcos(2x))	\frac{d}{dx}(3\sin^{2}(x)\cos(2x))
(\partial)/(\partial x)((x/(x-y))^{1/3})	\frac{\partial\:}{\partial\:x}((\frac{x}{x-y})^{\frac{1}{3}})
(\partial)/(\partial x)((x-y)/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{x-y}{(x+y)^{2}})
derivative of (x^2-10x/((x-5)^2))	\frac{d}{dx}(\frac{x^{2}-10x}{(x-5)^{2}})
derivative of f(x)=(2x)/(x^2+1)	derivative\:f(x)=\frac{2x}{x^{2}+1}
derivative of 3x^2-2x	derivative\:3x^{2}-2x
derivative of 7(4^x)	derivative\:7(4^{x})
limit as x approaches-5-of 1/(x^2-25)	\lim\:_{x\to\:-5-}(\frac{1}{x^{2}-25})
d/(dt)((5t)/(1+2t^2))	\frac{d}{dt}(\frac{5t}{1+2t^{2}})
(dy)/(dt)= 1/((y+1)(t-2)),y(0)=0	\frac{dy}{dt}=\frac{1}{(y+1)(t-2)},y(0)=0
integral of cos(5x)cos(10x)	\int\:\cos(5x)\cos(10x)dx
inverse oflaplace (e^{-s})/(((s-3)(s+1)))	inverselaplace\:\frac{e^{-s}}{((s-3)(s+1))}
derivative of 4x^{(-1/8})	\frac{d}{dx}(4x^{\frac{-1}{8}})
(\partial)/(\partial x)(5x^{0.75}y^{0.25})	\frac{\partial\:}{\partial\:x}(5x^{0.75}y^{0.25})
integral of ((ln(x))^{24})/x	\int\:\frac{(\ln(x))^{24}}{x}dx
f(x)=ln(x^{ln(x)})	f(x)=\ln(x^{\ln(x)})
integral from-infinity to-1 of e^{-20t}	\int\:_{-\infty\:}^{-1}e^{-20t}dt
derivative of \sqrt[3]{t^2}	derivative\:\sqrt[3]{t^{2}}
integral of x^2ln(x	\int\:x^{2}\ln(d)xdx
derivative of x*e^{-sin(x}-x)	\frac{d}{dx}(x\cdot\:e^{-\sin(x)}-x)
derivative of (x^2-3/(x-2))	\frac{d}{dx}(\frac{x^{2}-3}{x-2})
derivative of (2x)/(1-tan(x))	derivative\:\frac{2x}{1-\tan(x)}
xy^'+y=x^2-2x+1	xy^{\prime\:}+y=x^{2}-2x+1
derivative of sqrt(1+xe^{-2x)}	derivative\:\sqrt{1+xe^{-2x}}
derivative of 7(x-5)^{2/3}	derivative\:7(x-5)^{\frac{2}{3}}
integral from 1/2 to 7 of 6xln(2x)	\int\:_{\frac{1}{2}}^{7}6x\ln(2x)dx
integral from-infinity to-1 of e^{-2t}	\int\:_{-\infty\:}^{-1}e^{-2t}dt
d/(dy)(ln(x+y))	\frac{d}{dy}(\ln(x+y))
derivative of f(x)=2^{40}	derivative\:f(x)=2^{40}
area sin(x),cos(x),[-pi,pi]	area\:\sin(x),\cos(x),[-π,π]
integral of (20s+20)/((s^2+1)(s-1)^3)	\int\:\frac{20s+20}{(s^{2}+1)(s-1)^{3}}ds
derivative of (3-4x^{4/3})	\frac{d}{dx}((3-4x)^{\frac{4}{3}})
tangent of f(x)=[(x-2)^2-x]^2,\at x=3	tangent\:f(x)=[(x-2)^{2}-x]^{2},\at\:x=3
area 4-x^2,y=0	area\:4-x^{2},y=0
integral from 3 to 6 of 10000e^{0.02t}	\int\:_{3}^{6}10000e^{0.02t}dt
(\partial)/(\partial y)(sqrt(2x^2+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{2x^{2}+y^{2}})
limit as x approaches+2-of x/(x^2-4)	\lim\:_{x\to\:+2-}(\frac{x}{x^{2}-4})
integral of (1+x^2)*sqrt(1+64x^2)	\int\:(1+x^{2})\cdot\:\sqrt{1+64x^{2}}dx
tangent of f(x)=4sec(x),\at x= pi/6	tangent\:f(x)=4\sec(x),\at\:x=\frac{π}{6}
(2y^2x+3x)dx+(2x^2y)dy=0	(2y^{2}x+3x)dx+(2x^{2}y)dy=0
(\partial}{\partial v}(\frac{v^2)/u)	\frac{\partial\:}{\partial\:v}(\frac{v^{2}}{u})
derivative of sqrt(2-x)-sqrt(y+1)	\frac{d}{dx}(\sqrt{2-x}-\sqrt{y+1})
limit as x approaches 1 of 1+x^2	\lim\:_{x\to\:1}(1+x^{2})
derivative of 100	\frac{d}{dx}(100)
limit as x approaches 6 of (6/x-1)/(x-6)	\lim\:_{x\to\:6}(\frac{\frac{6}{x}-1}{x-6})
derivative of x/pi	\frac{d}{dx}(\frac{x}{π})
implicit (dy)/(dx), x/y =0	implicit\:\frac{dy}{dx},\frac{x}{y}=0
integral from 0 to 4 of x^4	\int\:_{0}^{4}x^{4}dx
area (4/x),(16x),(1/4 x)	area\:(\frac{4}{x}),(16x),(\frac{1}{4}x)
limit as x approaches 2+of 2/(x^2-4)	\lim\:_{x\to\:2+}(\frac{2}{x^{2}-4})
integral of (3^{5x}-1)/(3^{5x)}	\int\:\frac{3^{5x}-1}{3^{5x}}dx
derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x))	derivative\:3(5e^{5x}\cos(6x)-6e^{5x}\sin(6x))
sum from n=0 to infinity of (-1/6)^n	\sum\:_{n=0}^{\infty\:}(-\frac{1}{6})^{n}
integral of 1/(x^5sqrt(4x^2-1))	\int\:\frac{1}{x^{5}\sqrt{4x^{2}-1}}dx
integral of x/(sin^2(x))	\int\:\frac{x}{\sin^{2}(x)}dx
derivative of arcsin(x)	\frac{d}{dx}(\arcsin(x))
taylor 1-e^x	taylor\:1-e^{x}
(\partial)/(\partial x)((2xy^2)/(4+x^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{2xy^{2}}{4+x^{2}y^{2}})
limit as x approaches 0+of (e^{-1/x})/x	\lim\:_{x\to\:0+}(\frac{e^{-\frac{1}{x}}}{x})
limit as x approaches-2 of \|x\|	\lim\:_{x\to\:-2}(\left\|x\right\|)
tangent of f(x)= 7/(1-x),\at x=-3	tangent\:f(x)=\frac{7}{1-x},\at\:x=-3
derivative of 8z^2e^z	derivative\:8z^{2}e^{z}
(d^2)/(dx^2)((x^2+1)/(x^2-4))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}+1}{x^{2}-4})
integral of 7/(x-2)	\int\:\frac{7}{x-2}dx
tangent of e^{x^3}	tangent\:e^{x^{3}}
(\partial)/(\partial x)(e^{xyz^3})	\frac{\partial\:}{\partial\:x}(e^{xyz^{3}})
integral of tln(t+5)	\int\:t\ln(t+5)dt
integral of x/(1+2x^2)	\int\:\frac{x}{1+2x^{2}}dx
derivative of x^5+3x^2+1	\frac{d}{dx}(x^{5}+3x^{2}+1)
area 10x,x^2-11	area\:10x,x^{2}-11
derivative of 1-e^{-e^x}	\frac{d}{dx}(1-e^{-e^{x}})
y^'-8y=cos(x)	y^{\prime\:}-8y=\cos(x)
integral of x/(x^{2+1)}	\int\:\frac{x}{x^{2+1}}dx
derivative of acos(x+bsin(x))	\frac{d}{dx}(a\cos(x)+b\sin(x))
integral of sqrt(16-x^2)	\int\:\sqrt{16-x^{2}}dx
integral of (cos(4x))^2	\int\:(\cos(4x))^{2}dx
area y=x^3,y=0,x=1,x=2	area\:y=x^{3},y=0,x=1,x=2
integral from 0 to 19/6 of pi(19/6-x)^2	\int\:_{0}^{\frac{19}{6}}π(\frac{19}{6}-x)^{2}dx
tangent of f(x)=e^{8x}cos(pix),\at x=0	tangent\:f(x)=e^{8x}\cos(πx),\at\:x=0
(\partial)/(\partial z)(rcos(t))	\frac{\partial\:}{\partial\:z}(r\cos(t))
laplacetransform 1-2e^{-2t}	laplacetransform\:1-2e^{-2t}
integral of e^{4x}sqrt(1+e^{2x)}	\int\:e^{4x}\sqrt{1+e^{2x}}dx
limit as x approaches 3 of 2x^2+4x+1	\lim\:_{x\to\:3}(2x^{2}+4x+1)
y^{''}-2y^'+5y=25x^2+12	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=25x^{2}+12
integral from 0 to 2 of (3t)/((3-t)^2)	\int\:_{0}^{2}\frac{3t}{(3-t)^{2}}dt
tangent of y=3x^2+5x,(-3,-13)	tangent\:y=3x^{2}+5x,(-3,-13)
limit as x approaches 3 of e^x	\lim\:_{x\to\:3}(e^{x})
limit as x approaches infinity of tan(x)	\lim\:_{x\to\:\infty\:}(\tan(x))
derivative of ln(sqrt(x^2+3))	\frac{d}{dx}(\ln(\sqrt{x^{2}+3}))
derivative of 3^{(x^4+1^3})	\frac{d}{dx}(3^{(x^{4}+1)^{3}})
integral of sin(5x)cos(4x)	\int\:\sin(5x)\cos(4x)dx
integral of sec^2(x)tan^7(x)	\int\:\sec^{2}(x)\tan^{7}(x)dx
integral of (3x^2-5x+1)/((x-4))	\int\:\frac{3x^{2}-5x+1}{(x-4)}dx
maclaurin e^{x^5}	maclaurin\:e^{x^{5}}
derivative of f(x)=x^3-3x^2	derivative\:f(x)=x^{3}-3x^{2}
(d^2)/(dx^2)(sqrt(x)+\sqrt[3]{x})	\frac{d^{2}}{dx^{2}}(\sqrt{x}+\sqrt[3]{x})
integral of (x^2In^3(1+x^3))/(1+x^3)	\int\:\frac{x^{2}In^{3}(1+x^{3})}{1+x^{3}}dx

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