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Popular Calculus Problems

limit as x approaches-2+of-1/(x^2-4)	\lim\:_{x\to\:-2+}(-\frac{1}{x^{2}-4})
derivative of-ax+d/(x^2)	\frac{d}{dx}(-ax+\frac{d}{x^{2}})
inverse oflaplace s/((s^2+1)(s^2-2s+2))	inverselaplace\:\frac{s}{(s^{2}+1)(s^{2}-2s+2)}
integral of (x-5)/(x^2+9)	\int\:\frac{x-5}{x^{2}+9}dx
integral of x^2sin(2Ax)	\int\:x^{2}\sin(2Ax)dx
(dy)/(dx)=sqrt(4y)e^{x+10}	\frac{dy}{dx}=\sqrt{4y}e^{x+10}
derivative of (2x+2x^{1/2}/(6+x^{3/2)})	\frac{d}{dx}(\frac{2x+2x^{\frac{1}{2}}}{6+x^{\frac{3}{2}}})
integral of x^3cos(5x)	\int\:x^{3}\cos(5x)dx
integral of 20x^9	\int\:20x^{9}dx
tangent of f(x)=4sqrt(x)-1,\at x=16	tangent\:f(x)=4\sqrt{x}-1,\at\:x=16
area y=3x,y=x^2-4	area\:y=3x,y=x^{2}-4
y^'=x+6y	y^{\prime\:}=x+6y
derivative of ln(x/3+(x-3)/x)	\frac{d}{dx}(\ln(\frac{x}{3})+\frac{x-3}{x})
inverse oflaplace 3/(s(s-1)^3)	inverselaplace\:\frac{3}{s(s-1)^{3}}
f(x)=log_{10}(sqrt(1-x))	f(x)=\log_{10}(\sqrt{1-x})
integral of 30x	\int\:30xdx
derivative of a-b(x-c^{1/3})	\frac{d}{dx}(a-b(x-c)^{\frac{1}{3}})
integral of (x+1)e^{3x}	\int\:(x+1)e^{3x}dx
derivative of 1/2 tan^2(x)	\frac{d}{dx}(\frac{1}{2}\tan^{2}(x))
integral of sqrt(e^x-3)	\int\:\sqrt{e^{x}-3}dx
integral from-1 to 5 of (8x)/(x^2-4x-12)	\int\:_{-1}^{5}\frac{8x}{x^{2}-4x-12}dx
(\partial)/(\partial z)(x/y-y/z)	\frac{\partial\:}{\partial\:z}(\frac{x}{y}-\frac{y}{z})
integral of 1/((x-4)^{3/2)}	\int\:\frac{1}{(x-4)^{\frac{3}{2}}}dx
limit as x approaches 0 of x^{-5/(ln(x))}	\lim\:_{x\to\:0}(x^{-\frac{5}{\ln(x)}})
(\partial)/(\partial x)(x^2+3y^2)	\frac{\partial\:}{\partial\:x}(x^{2}+3y^{2})
tangent of f(x)=x^2+8,(5,33)	tangent\:f(x)=x^{2}+8,(5,33)
tangent of y= 8/x ,(2,4)	tangent\:y=\frac{8}{x},(2,4)
limit as x approaches infinity of x^3+x	\lim\:_{x\to\:\infty\:}(x^{3}+x)
integral of (4x+13)/(x^2+3x-10)	\int\:\frac{4x+13}{x^{2}+3x-10}dx
(\partial)/(\partial x)(2x^2y+2x)	\frac{\partial\:}{\partial\:x}(2x^{2}y+2x)
integral from 0 to 1 of xe^{-2x^2}	\int\:_{0}^{1}xe^{-2x^{2}}dx
slope of (-29)(-2-5)	slope\:(-29)(-2-5)
limit as x approaches-infinity of 3x^6	\lim\:_{x\to\:-\infty\:}(3x^{6})
inverse oflaplace (4s+20)/(s^2+8s+16)	inverselaplace\:\frac{4s+20}{s^{2}+8s+16}
(d^2)/(dx^2)(8/(9t^6))	\frac{d^{2}}{dx^{2}}(\frac{8}{9t^{6}})
(\partial)/(\partial y)(x^4)	\frac{\partial\:}{\partial\:y}(x^{4})
integral of 4	\int\:4dx
derivative of f(x)=(5x+1)^2	derivative\:f(x)=(5x+1)^{2}
area 32-8x,[2,4]	area\:32-8x,[2,4]
derivative of y=12sqrt(x)	derivative\:y=12\sqrt{x}
y^'=10xy-2x	y^{\prime\:}=10xy-2x
integral from-infinity to 0 of 1/(2-3x)	\int\:_{-\infty\:}^{0}\frac{1}{2-3x}dx
derivative of 1/((x-1^2+1))	\frac{d}{dx}(\frac{1}{(x-1)^{2}+1})
x^2 derivative of (dy/(dx))+19x(dy)/(dx)+145y=0	x^{2}\frac{d}{dx}(\frac{dy}{dx})+19x\frac{dy}{dx}+145y=0
5y^{''}+11y^'+7y=0,y(0)=8,y^'(0)=10	5y^{\prime\:\prime\:}+11y^{\prime\:}+7y=0,y(0)=8,y^{\prime\:}(0)=10
integral from 0 to 1 of 4x^3sqrt(3x^4+4)	\int\:_{0}^{1}4x^{3}\sqrt{3x^{4}+4}dx
integral of xsqrt((1-x^2))	\int\:x\sqrt{(1-x^{2})}dx
derivative of sqrt(1/(x^2-2))	\frac{d}{dx}(\sqrt{\frac{1}{x^{2}-2}})
(\partial)/(\partial x)(x^2+y^2+2xy)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+2xy)
integral of 7e^{-0.8x}	\int\:7e^{-0.8x}dx
limit as x approaches infinity of x 1/2	\lim\:_{x\to\:\infty\:}(x\frac{1}{2})
limit as x approaches 0 of x^2csc^2(x/2)	\lim\:_{x\to\:0}(x^{2}\csc^{2}(\frac{x}{2}))
slope of (-9,6),(-6,-9)	slope\:(-9,6),(-6,-9)
integral of r^4(7-(r^5)/(10))^3	\int\:r^{4}(7-\frac{r^{5}}{10})^{3}dr
y^'=(3t^2-e^t)/(2y-5)	y^{\prime\:}=\frac{3t^{2}-e^{t}}{2y-5}
integral of \sqrt[3]{t}(5t^2-3t+2)	\int\:\sqrt[3]{t}(5t^{2}-3t+2)dt
sum from n=1 to infinity of 3n+1	\sum\:_{n=1}^{\infty\:}3n+1
integral from 0 to 1 of sqrt(1+(2x)^2)	\int\:_{0}^{1}\sqrt{1+(2x)^{2}}dx
derivative of y=3+5sqrt(x)	derivative\:y=3+5\sqrt{x}
(\partial)/(\partial x)(cosh(x))	\frac{\partial\:}{\partial\:x}(\cosh(x))
integral of (5r^2)/(r+1)	\int\:\frac{5r^{2}}{r+1}dr
tangent of f(x)=9x^2+5	tangent\:f(x)=9x^{2}+5
sum from n=0 to infinity of 1/(n^{3/2)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{\frac{3}{2}}}
area (x^3-11x^2+30x),(-x^3+11x^2-30x)	area\:(x^{3}-11x^{2}+30x),(-x^{3}+11x^{2}-30x)
derivative of log_{3}((x^2/(x+1)))	\frac{d}{dx}(\log_{3}(\frac{x^{2}}{x+1}))
(dy)/(dx)=-4(y-3)	\frac{dy}{dx}=-4(y-3)
(\partial)/(\partial x)(2x+y^6)	\frac{\partial\:}{\partial\:x}(2x+y^{6})
integral of sin^2(x/2)	\int\:\sin^{2}(\frac{x}{2})dx
derivative of f(x)=ln(x+sqrt(3+x^2))	derivative\:f(x)=\ln(x+\sqrt{3+x^{2}})
integral of-x/(y^2)	\int\:-\frac{x}{y^{2}}dy
(dy)/(dx)+10(tan(10x))y=-cos(10x)	\frac{dy}{dx}+10(\tan(10x))y=-\cos(10x)
integral of ((x^3))/(sqrt(x^2+100))	\int\:\frac{(x^{3})}{\sqrt{x^{2}+100}}dx
derivative of e^{rx}	derivative\:e^{rx}
derivative of-e^{-x}x^2+6e^{-x}x-6e^{-x}	\frac{d}{dx}(-e^{-x}x^{2}+6e^{-x}x-6e^{-x})
integral of cot^3(10x)	\int\:\cot^{3}(10x)dx
2(d^2y)/(dx^2)+2(dy)/(dx)+y=1	2\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+y=1
derivative of cos(x^3+2x)	\frac{d}{dx}(\cos(x^{3}+2x))
derivative of 3x^{4/3}-2x^{1/7}	derivative\:3x^{\frac{4}{3}}-2x^{\frac{1}{7}}
limit as x approaches-3 of ((x^2+7x+12))/(x^2-9)	\lim\:_{x\to\:-3}(\frac{(x^{2}+7x+12)}{x^{2}-9})
limit as x approaches 3 of (x^2-9)/(x+1)	\lim\:_{x\to\:3}(\frac{x^{2}-9}{x+1})
integral of 4cos(6x)	\int\:4\cos(6x)dx
integral of-(3x)/2	\int\:-\frac{3x}{2}dx
integral of 2/(x^3+x)	\int\:\frac{2}{x^{3}+x}dx
integral from 0 to 2 of sqrt(4-x^2)	\int\:_{0}^{2}\sqrt{4-x^{2}}dx
(\partial)/(\partial y)(xy^2)	\frac{\partial\:}{\partial\:y}(xy^{2})
derivative of 3ln(2x)	derivative\:3\ln(2x)
integral of (sin^2(1/x))/(x^2)	\int\:\frac{\sin^{2}(\frac{1}{x})}{x^{2}}dx
derivative of 10^6x^2e^{-x}	\frac{d}{dx}(10^{6}\cdot\:x^{2}\cdot\:e^{-x})
integral of (e^{2t})/(sqrt(e^{2t)+4)}	\int\:\frac{e^{2t}}{\sqrt{e^{2t}+4}}dt
d/(d{y)}(10e^{{x}}sin({y}){z}^3)	\frac{d}{d{y}}(10e^{{x}}\sin({y}){z}^{3})
d/(dt)(5t^{-3/5})	\frac{d}{dt}(5t^{-\frac{3}{5}})
integral of 1/(x+sqrt(x))	\int\:\frac{1}{x+\sqrt{x}}dx
integral of ((x^2))/(1+x^3)	\int\:\frac{(x^{2})}{1+x^{3}}dx
limit as x approaches-1 of 3x^2-2x-1	\lim\:_{x\to\:-1}(3x^{2}-2x-1)
tangent of f(x)=3-x^2+2x	tangent\:f(x)=3-x^{2}+2x
tangent of f(x)=8x^2+4x-6,\at x=-3	tangent\:f(x)=8x^{2}+4x-6,\at\:x=-3
integral of (u-2u^2)/(sqrt(u))	\int\:\frac{u-2u^{2}}{\sqrt{u}}du
integral of ae^x	\int\:ae^{x}dx
integral of 8/(sqrt(e^x-2))	\int\:\frac{8}{\sqrt{e^{x}-2}}dx
integral from-infinity to 15 of re^{r/5}	\int\:_{-\infty\:}^{15}re^{\frac{r}{5}}dr

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