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Popular Calculus Problems

limit as x approaches infinity of e^x+3	\lim\:_{x\to\:\infty\:}(e^{x}+3)
integral from 0 to infinity of e^{-x/4}	\int\:_{0}^{\infty\:}e^{-\frac{x}{4}}dx
limit as x approaches 0 of (1+x)^{2/x}	\lim\:_{x\to\:0}((1+x)^{\frac{2}{x}})
integral of \sqrt[5]{tan(6x)}sec^2(6x)	\int\:\sqrt[5]{\tan(6x)}\sec^{2}(6x)dx
derivative of 4e^{3x}+12xe^{3x}	\frac{d}{dx}(4e^{3x}+12xe^{3x})
laplacetransform sin(5t)	laplacetransform\:\sin(5t)
(\partial)/(\partial x)(-3xy(-3-x-y))	\frac{\partial\:}{\partial\:x}(-3xy(-3-x-y))
(dy)/(dx)=((x^2+y))/(x^3)	\frac{dy}{dx}=\frac{(x^{2}+y)}{x^{3}}
f(x)=ln(x+2)	f(x)=\ln(x+2)
integral from 8 to 9 of 1/(x^2-1)	\int\:_{8}^{9}\frac{1}{x^{2}-1}dx
area y=sqrt(9-x^2),0<= x<= 2	area\:y=\sqrt{9-x^{2}},0\le\:x\le\:2
tangent of f(x)=7e^{x^2-9x+8},\at x=0	tangent\:f(x)=7e^{x^{2}-9x+8},\at\:x=0
derivative of y=164sqrt(4x^4)+4	derivative\:y=164\sqrt{4x^{4}}+4
y^{''}+6y^'+5y=10	y^{\prime\:\prime\:}+6y^{\prime\:}+5y=10
integral of 1/h	\int\:\frac{1}{h}dh
simplify (x^4)/4+(x^3)/3-(x^2)/2-5	simplify\:\frac{x^{4}}{4}+\frac{x^{3}}{3}-\frac{x^{2}}{2}-5
integral of x^2*e^{-x^3}	\int\:x^{2}\cdot\:e^{-x^{3}}dx
integral of (e^x)/((e^x-1)(e^{2x)+1)}	\int\:\frac{e^{x}}{(e^{x}-1)(e^{2x}+1)}dx
tangent of x/(x^2+64)	tangent\:\frac{x}{x^{2}+64}
limit as x approaches 3 of ((x^2-6))/((x-9))	\lim\:_{x\to\:3}(\frac{(x^{2}-6)}{(x-9)})
derivative of log_{6}(3x^3+4x^2+4x)	\frac{d}{dx}(\log_{6}(3x^{3}+4x^{2}+4x))
integral of sqrt(64-5x^2)	\int\:\sqrt{64-5x^{2}}dx
integral of ((x^2))/(sqrt(20-4x+x^2))	\int\:\frac{(x^{2})}{\sqrt{20-4x+x^{2}}}dx
integral of (ln(16x))/x	\int\:\frac{\ln(16x)}{x}dx
y^'=(e^t)/(2y)	y^{\prime\:}=\frac{e^{t}}{2y}
integral of (sin^4(x)cos(x))	\int\:(\sin^{4}(x)\cos(x))dx
tangent of f(x)=x^2-4,(-5,21)	tangent\:f(x)=x^{2}-4,(-5,21)
sum from n=1 to infinity of 6/n	\sum\:_{n=1}^{\infty\:}\frac{6}{n}
derivative of sqrt(2+\sqrt{6x)}	\frac{d}{dx}(\sqrt{2+\sqrt{6x}})
d/(dy)(y^y)	\frac{d}{dy}(y^{y})
derivative of e^{3x^2}+ln(5x-4)	\frac{d}{dx}(e^{3x^{2}}+\ln(5x-4))
derivative of x-sin^2(x-4)	\frac{d}{dx}(x-\sin^{2}(x)-4)
derivative of (4sin(x))/(6-7sin(x))	derivative\:\frac{4\sin(x)}{6-7\sin(x)}
(\partial)/(\partial x)(e^{-x}cos(-8y))	\frac{\partial\:}{\partial\:x}(e^{-x}\cos(-8y))
derivative of f(x)=(12)/(ln(x))	derivative\:f(x)=\frac{12}{\ln(x)}
inverse oflaplace 1/((s^2+3s+2))	inverselaplace\:\frac{1}{(s^{2}+3s+2)}
limit as x approaches infinity of cos(x)	\lim\:_{x\to\:\infty\:}(\cos(x))
integral from-2 to 3 of (20)/(x^4)	\int\:_{-2}^{3}\frac{20}{x^{4}}dx
(\partial)/(\partial y)(sqrt(x+yz))	\frac{\partial\:}{\partial\:y}(\sqrt{x+yz})
derivative of x^2sqrt(x^2-9)	\frac{d}{dx}(x^{2}\sqrt{x^{2}-9})
limit as x approaches 12 of (x^3)/3	\lim\:_{x\to\:12}(\frac{x^{3}}{3})
(\partial)/(\partial y)(x+y-320)	\frac{\partial\:}{\partial\:y}(x+y-320)
(\partial)/(\partial x)(x^4+y^3)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{3})
taylor 1/(1+x),0	taylor\:\frac{1}{1+x},0
sum from n=1 to infinity of (-9^n)/(n^4)	\sum\:_{n=1}^{\infty\:}\frac{-9^{n}}{n^{4}}
integral of (x^2+2x)*3^x	\int\:(x^{2}+2x)\cdot\:3^{x}dx
integral from-3 to 3 of (13-x^2)-(x^2-5)	\int\:_{-3}^{3}(13-x^{2})-(x^{2}-5)dx
integral of 1/(sqrt(x^2+169))	\int\:\frac{1}{\sqrt{x^{2}+169}}dx
(2x+1)((dy)/(dx))+y=(2x+1)^{3/2}	(2x+1)(\frac{dy}{dx})+y=(2x+1)^{\frac{3}{2}}
y^{''}+3y=-48x^2e^{3x}	y^{\prime\:\prime\:}+3y=-48x^{2}e^{3x}
f(x)=arcsinh(x)	f(x)=\arcsinh(x)
inverse oflaplace e^{(-4s)}	inverselaplace\:e^{(-4s)}
integral of-510x^2+3414x+1998	\int\:-510x^{2}+3414x+1998dx
limit as x approaches infinity of (sqrt(225x^2+7x-23))/(15x)	\lim\:_{x\to\:\infty\:}(\frac{\sqrt{225x^{2}+7x-23}}{15x})
integral of cos(x)sqrt(x)	\int\:\cos(x)\sqrt{x}dx
derivative of f(x)=(9-x^3)^{-2}	derivative\:f(x)=(9-x^{3})^{-2}
10y^{''}+2y^'+5y=0	10y^{\prime\:\prime\:}+2y^{\prime\:}+5y=0
(dy}{dx}=\frac{4y)/x	\frac{dy}{dx}=\frac{4y}{x}
derivative of ln(sqrt(x+4))	derivative\:\ln(\sqrt{x+4})
(xy-y^2)dx+x^3dy=0	(xy-y^{2})dx+x^{3}dy=0
tangent of f(x)=3x^2-3x	tangent\:f(x)=3x^{2}-3x
derivative of y=(sqrt(x))/(1+x)	derivative\:y=\frac{\sqrt{x}}{1+x}
integral of 1/(x^2+10x+41)	\int\:\frac{1}{x^{2}+10x+41}dx
slope of (0,-3),(-3,0)	slope\:(0,-3),(-3,0)
(dy)/(dx)=((x+y^2))/(2y)	\frac{dy}{dx}=\frac{(x+y^{2})}{2y}
(\partial)/(\partial x)(x^ay^b)	\frac{\partial\:}{\partial\:x}(x^{a}y^{b})
(\partial}{\partial x}(\frac{(2x))/y)	\frac{\partial\:}{\partial\:x}(\frac{(2x)}{y})
y^{''}-4y=6e^t	y^{\prime\:\prime\:}-4y=6e^{t}
area 5cos(2x),5-5cos(2x),0, pi/2	area\:5\cos(2x),5-5\cos(2x),0,\frac{π}{2}
integral of (20x^3)/(4+5x^4)	\int\:\frac{20x^{3}}{4+5x^{4}}dx
y^{''}+4y=t*sin(2t)	y^{\prime\:\prime\:}+4y=t\cdot\:\sin(2t)
derivative of 2+5arctan(x/2)	derivative\:2+5\arctan(\frac{x}{2})
derivative of 1/((x+6)^2)	derivative\:\frac{1}{(x+6)^{2}}
xy^'+y=yy	xy^{\prime\:}+y=yy
(\partial)/(\partial y)(x^2-yx)	\frac{\partial\:}{\partial\:y}(x^{2}-yx)
derivative of (2x)/(x+1)	derivative\:\frac{2x}{x+1}
integral of 1/(e^{-2y)}	\int\:\frac{1}{e^{-2y}}dy
integral from 0 to 1/2 of 30x	\int\:_{0}^{\frac{1}{2}}30xdx
derivative of (x+1/(sqrt(x^2+1)))	\frac{d}{dx}(\frac{x+1}{\sqrt{x^{2}+1}})
integral of 1/4 x^4	\int\:\frac{1}{4}x^{4}dx
derivative of e^{-2x}-2e^{-2x}x	\frac{d}{dx}(e^{-2x}-2e^{-2x}x)
d/(dt)(-1cos(t)+8sin(t))	\frac{d}{dt}(-1\cos(t)+8\sin(t))
integral from 0 to 1 of 4sqrt(x)-4x	\int\:_{0}^{1}4\sqrt{x}-4xdx
integral of (x^5)/((3-x^6)^4)	\int\:\frac{x^{5}}{(3-x^{6})^{4}}dx
y^{''}+7y^'+12y=0	y^{\prime\:\prime\:}+7y^{\prime\:}+12y=0
sum from n=5 to infinity of (n!)/(n^n)	\sum\:_{n=5}^{\infty\:}\frac{n!}{n^{n}}
integral of 1/(sqrt(-t^2+6t-8))	\int\:\frac{1}{\sqrt{-t^{2}+6t-8}}dt
derivative of 0.006x^3+0.02x^2+0.5x	\frac{d}{dx}(0.006x^{3}+0.02x^{2}+0.5x)
d/(dy)(ycos(x)y)	\frac{d}{dy}(y\cos(x)y)
tangent of 3x^2-9	tangent\:3x^{2}-9
y^'=(e^x)/(y^2)	y^{\prime\:}=\frac{e^{x}}{y^{2}}
(\partial)/(\partial x)(2y+z)	\frac{\partial\:}{\partial\:x}(2y+z)
integral of (sqrt(x))/(x+4)	\int\:\frac{\sqrt{x}}{x+4}dx
integral from 0 to 3 of 5x	\int\:_{0}^{3}5xdx
integral of 1/(sqrt(x^2-64))	\int\:\frac{1}{\sqrt{x^{2}-64}}dx
limit as x approaches-2 of sqrt(8+1^3)	\lim\:_{x\to\:-2}(\sqrt{8+1^{3}})
derivative of (2x^2+5(5x-3))	\frac{d}{dx}((2x^{2}+5)(5x-3))
(dy)/(dx)=(x+y)/(y-x)	\frac{dy}{dx}=\frac{x+y}{y-x}
tangent of f(x)=10x^3-45x^2+60x-30	tangent\:f(x)=10x^{3}-45x^{2}+60x-30
d/(ds)(((s^2-4s+20))/(s^2+6s+8))	\frac{d}{ds}(\frac{(s^{2}-4s+20)}{s^{2}+6s+8})

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