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Popular Calculus Problems

derivative of ln(5e^{-4x})	\frac{d}{dx}(\ln(5e^{-4x}))
integral of x/(x^2+4x+3)	\int\:\frac{x}{x^{2}+4x+3}dx
integral of 1/(4-y)	\int\:\frac{1}{4-y}dy
limit as x approaches 8+of (x-8)/(\|x-8\|)	\lim\:_{x\to\:8+}(\frac{x-8}{\left\|x-8\right\|})
tangent of y=3x^2-2x,\at x=-1	tangent\:y=3x^{2}-2x,\at\:x=-1
derivative of x^2(x-2^4)	\frac{d}{dx}(x^{2}(x-2)^{4})
(\partial)/(\partial x)(sqrt(2x+3y))	\frac{\partial\:}{\partial\:x}(\sqrt{2x+3y})
limit as x approaches infinity of 3/3	\lim\:_{x\to\:\infty\:}(\frac{3}{3})
derivative of x^{ln(5})	\frac{d}{dx}(x^{\ln(5)})
sum from n=0 to infinity of 1/(n^2+5n+6)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+5n+6}
integral of (5x^2+6+9/(x^2+1))	\int\:(5x^{2}+6+\frac{9}{x^{2}+1})dx
(dh)/(dt)+1/2 h=1	\frac{dh}{dt}+\frac{1}{2}h=1
derivative of \sqrt[4]{sin(x^3})	\frac{d}{dx}(\sqrt[4]{\sin(x^{3})})
integral of e^{cos(6t)}sin(6t)	\int\:e^{\cos(6t)}\sin(6t)dt
y^{''}-4y^'+4y=0,y(0)=-4,y^'(0)=4	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=0,y(0)=-4,y^{\prime\:}(0)=4
integral of 1/(100+2t)	\int\:\frac{1}{100+2t}dt
limit as x approaches+0 of 3x	\lim\:_{x\to\:+0}(3x)
(\partial)/(\partial y)(1+ye^{xy})	\frac{\partial\:}{\partial\:y}(1+ye^{xy})
integral from 1 to 4 of (sqrt(x)ln(x))	\int\:_{1}^{4}(\sqrt{x}\ln(x))dx
derivative of ye^{-x}	\frac{d}{dx}(ye^{-x})
(dP)/(dt)=aP-bP^2	\frac{dP}{dt}=aP-bP^{2}
limit as x approaches 2 of ((x+3))/(x-2)	\lim\:_{x\to\:2}(\frac{(x+3)}{x-2})
(dy)/(dx)=(e^x)/(6+e^x)	\frac{dy}{dx}=\frac{e^{x}}{6+e^{x}}
area cos(x),0.5,0<= x<= pi	area\:\cos(x),0.5,0\le\:x\le\:π
integral of (2x-3)tan(7x^2-21x+9)	\int\:(2x-3)\tan(7x^{2}-21x+9)dx
derivative of y=(x+6)/(x^3+x-7)	derivative\:y=\frac{x+6}{x^{3}+x-7}
(y^4-x^2)(dy)/(dx)=-x*y	(y^{4}-x^{2})\frac{dy}{dx}=-x\cdot\:y
(x^2+1)((dy)/(dx))+3x(y-1)=0	(x^{2}+1)(\frac{dy}{dx})+3x(y-1)=0
(\partial)/(\partial x)(7xln(xy))	\frac{\partial\:}{\partial\:x}(7x\ln(xy))
derivative of 13^x	\frac{d}{dx}(13^{x})
integral from 2 to 4 of 1/(\|x-3\|^{1/2)}	\int\:_{2}^{4}\frac{1}{\left\|x-3\right\|^{\frac{1}{2}}}dx
tangent of f(x)=x^2+x,\at x=-4,-1	tangent\:f(x)=x^{2}+x,\at\:x=-4,-1
integral of-2/y	\int\:-\frac{2}{y}dy
integral from 2 to 5 of 4/(9+(x-2)^2)	\int\:_{2}^{5}\frac{4}{9+(x-2)^{2}}dx
derivative of f(x)=ln(169sin^2(x))	derivative\:f(x)=\ln(169\sin^{2}(x))
integral of e^{tan(8x)}sec^2(8x)	\int\:e^{\tan(8x)}\sec^{2}(8x)dx
derivative of 8sqrt(x)+6x^{3/4}	\frac{d}{dx}(8\sqrt{x}+6x^{\frac{3}{4}})
integral of 4/(1+x)	\int\:\frac{4}{1+x}dx
integral of (2x-1)ln(x)	\int\:(2x-1)\ln(x)dx
integral of (2x^2+x+15)/(x+3)	\int\:\frac{2x^{2}+x+15}{x+3}dx
integral from 1 to 2 of 2-x	\int\:_{1}^{2}2-xdx
y^'=xsqrt(y+3)	y^{\prime\:}=x\sqrt{y+3}
limit as x approaches-infinity of 2+e^x	\lim\:_{x\to\:-\infty\:}(2+e^{x})
derivative of 0.1x	\frac{d}{dx}(0.1x)
tangent of y=x^2+2,(2,6)	tangent\:y=x^{2}+2,(2,6)
integral of sqrt(1-r^2)	\int\:\sqrt{1-r^{2}}dr
area x^2,-x^2+18x	area\:x^{2},-x^{2}+18x
derivative of e^x-8x^7	derivative\:e^{x}-8x^{7}
inverse oflaplace {(2s-6)/(s^2+9)}	inverselaplace\:\left\{\frac{2s-6}{s^{2}+9}\right\}
derivative of ((x^3))/3+x	derivative\:\frac{(x^{3})}{3}+x
integral from 8 to 11 of 2arccot(x)	\int\:_{8}^{11}2\arccot(x)dx
laplacetransform t^2e^{-2t}sin(2t)	laplacetransform\:t^{2}e^{-2t}\sin(2t)
(\partial)/(\partial x)(2x+y)	\frac{\partial\:}{\partial\:x}(2x+y)
7y^'-14y=0	7y^{\prime\:}-14y=0
integral of sqrt(tan(x))	\int\:\sqrt{\tan(x)}dx
derivative of (-3)/(2x)	derivative\:\frac{-3}{2x}
integral of (x^2)/(\sqrt[4]{x^3+2)}	\int\:\frac{x^{2}}{\sqrt[4]{x^{3}+2}}dx
x(dy)/(dx)=y^2+y	x\frac{dy}{dx}=y^{2}+y
integral from 0 to 4 of sqrt(x)-1	\int\:_{0}^{4}\sqrt{x}-1dx
derivative of y=sqrt(5-x^2)	derivative\:y=\sqrt{5-x^{2}}
integral of (6x+5)sqrt(3x^2+5x)	\int\:(6x+5)\sqrt{3x^{2}+5x}dx
limit as t approaches 0 of (4t^2+3t+2)/(t^3+2t-6)	\lim\:_{t\to\:0}(\frac{4t^{2}+3t+2}{t^{3}+2t-6})
f(x)=-x^2+3x-1	f(x)=-x^{2}+3x-1
integral of ((e^{2x}))/(e^{4x)+4}	\int\:\frac{(e^{2x})}{e^{4x}+4}dx
integral of 1/(sqrt(8-2x-x^2))	\int\:\frac{1}{\sqrt{8-2x-x^{2}}}dx
derivative of 3/2	\frac{d}{dx}(\frac{3}{2})
(\partial)/(\partial x)(3e)	\frac{\partial\:}{\partial\:x}(3e)
y^{''}+y=tan^3(x)	y^{\prime\:\prime\:}+y=\tan^{3}(x)
integral of e^{-3x}sin(bx)	\int\:e^{-3x}\sin(bx)dx
(\partial)/(\partial x)((x^2+y^2)^2)	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{2})
integral of e^{4x-9}	\int\:e^{4x-9}dx
derivative of 3/(e^x+e^{-x})	\frac{d}{dx}(\frac{3}{e^{x}+e^{-x}})
derivative of 2/(sqrt(x^3+1))	\frac{d}{dx}(\frac{2}{\sqrt{x^{3}+1}})
y-xy^'=a(1+x^2y^')	y-xy^{\prime\:}=a(1+x^{2}y^{\prime\:})
limit as x approaches 3 of (2x-9)/(x-3)	\lim\:_{x\to\:3}(\frac{2x-9}{x-3})
(\partial)/(\partial x)(x^3yz^2+8yz)	\frac{\partial\:}{\partial\:x}(x^{3}yz^{2}+8yz)
integral of 1/(cos^2(x)+5cos(x)+6)	\int\:\frac{1}{\cos^{2}(x)+5\cos(x)+6}dx
integral of 10x^3+2x^2+1/2 x+3	\int\:10x^{3}+2x^{2}+\frac{1}{2}x+3dx
(dy)/(dx)=(y-5)^2	\frac{dy}{dx}=(y-5)^{2}
(dy)/(dx)	\frac{dy}{dx}
derivative of (-14x)/(12y)	derivative\:\frac{-14x}{12y}
area y= 1/2 x^2,y=-x^2+6	area\:y=\frac{1}{2}x^{2},y=-x^{2}+6
integral of x*ln(x-1)	\int\:x\cdot\:\ln(x-1)dx
2x(dy)/(dx)-y=3x^2	2x\frac{dy}{dx}-y=3x^{2}
limit as x approaches 2 of 1/(2x)	\lim\:_{x\to\:2}(\frac{1}{2x})
integral of 3x^2e^{9x^3}	\int\:3x^{2}e^{9x^{3}}dx
derivative of f(x)=sqrt((x-1)/(x+3))	derivative\:f(x)=\sqrt{\frac{x-1}{x+3}}
integral from 0 to infinity of e^{(-2x)}	\int\:_{0}^{\infty\:}e^{(-2x)}dx
derivative of 4^{(x^9)}	derivative\:4^{(x^{9})}
taylor 1/((2+x)^3)	taylor\:\frac{1}{(2+x)^{3}}
limit as x approaches-infinity of 3^{-x}	\lim\:_{x\to\:-\infty\:}(3^{-x})
slope of (11/6 ,-1/2),(1/3 , 1/3)	slope\:(\frac{11}{6},-\frac{1}{2}),(\frac{1}{3},\frac{1}{3})
slope of (1)(3.5)	slope\:(1)(3.5)
integral of 19arctan(x)	\int\:19\arctan(x)dx
f(x)=(4x^2-6x)^3	f(x)=(4x^{2}-6x)^{3}
derivative of y=(7x^3-3x^2-9)/(x^8)	derivative\:y=\frac{7x^{3}-3x^{2}-9}{x^{8}}
derivative of cos^2(x*sin(x))	\frac{d}{dx}(\cos^{2}(x)\cdot\:\sin(x))
integral from 0 to 4 of 6x	\int\:_{0}^{4}6xdx
tangent of f(x)=x^{1/2},(25,5)	tangent\:f(x)=x^{\frac{1}{2}},(25,5)
derivative of log_{2}(\sqrt[3]{2x+1})	\frac{d}{dx}(\log_{2}(\sqrt[3]{2x+1}))

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