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Popular Calculus Problems

derivative of (sqrt(x)-2(3sqrt(x)+8))	\frac{d}{dx}((\sqrt{x}-2)(3\sqrt{x}+8))
integral of (x+2)/(5x+6)	\int\:\frac{x+2}{5x+6}dx
derivative of e^xcos(x-sin(x)e^x)	\frac{d}{dx}(e^{x}\cos(x)-\sin(x)e^{x})
y^{''}+36y^'=0	y^{\prime\:\prime\:}+36y^{\prime\:}=0
limit as x approaches pi/2+of sec(x)	\lim\:_{x\to\:\frac{π}{2}+}(\sec(x))
integral of x(sqrt(9-x^2))	\int\:x(\sqrt{9-x^{2}})dx
tangent of f(x)=(5x)/(x+2),(3,3)	tangent\:f(x)=\frac{5x}{x+2},(3,3)
integral from 0 to 4 of x/8	\int\:_{0}^{4}\frac{x}{8}dx
tangent of f(x)=e^x-xe^x,\at x=0	tangent\:f(x)=e^{x}-xe^{x},\at\:x=0
limit as x approaches-11 of x^2+11	\lim\:_{x\to\:-11}(x^{2}+11)
limit as x approaches 0 of arctan(e^x)	\lim\:_{x\to\:0}(\arctan(e^{x}))
integral from 2 to 3 of 1/((x+1)ln(x+1))	\int\:_{2}^{3}\frac{1}{(x+1)\ln(x+1)}dx
integral of (csc^2(x))/(cot^4(x))	\int\:\frac{\csc^{2}(x)}{\cot^{4}(x)}dx
derivative of f(x)=10x^3-20x+1/5	derivative\:f(x)=10x^{3}-20x+\frac{1}{5}
y^{''}+y= 1/4 sin(3t)-3/4 sin(t)	y^{\prime\:\prime\:}+y=\frac{1}{4}\sin(3t)-\frac{3}{4}\sin(t)
derivative of arccos((ax/2))	\frac{d}{dx}(\arccos(\frac{ax}{2}))
integral of 1/x-4/(x^2+1)	\int\:\frac{1}{x}-\frac{4}{x^{2}+1}dx
integral from 0 to infinity of cos^2(x)	\int\:_{0}^{\infty\:}\cos^{2}(x)dx
integral of 1/(64e^{-8x)+e^{8x}}	\int\:\frac{1}{64e^{-8x}+e^{8x}}dx
slope of (5,7),(-4,-2)	slope\:(5,7),(-4,-2)
integral of (e^{4x}+e^{-4x})^2	\int\:(e^{4x}+e^{-4x})^{2}dx
derivative of f(x)=-(10)/(x^2)	derivative\:f(x)=-\frac{10}{x^{2}}
integral of 8-2x^2	\int\:8-2x^{2}dx
(\partial)/(\partial y)(4arctan(x/y))	\frac{\partial\:}{\partial\:y}(4\arctan(\frac{x}{y}))
derivative of (x^2-2x-48/(x+6))	\frac{d}{dx}(\frac{x^{2}-2x-48}{x+6})
derivative of f(x)=4x^2-2x+3	derivative\:f(x)=4x^{2}-2x+3
parity tan(3x)+x^4	parity\:\tan(3x)+x^{4}
y^{''}+11y^'+28y=84x^2+66x+6+40e^x	y^{\prime\:\prime\:}+11y^{\prime\:}+28y=84x^{2}+66x+6+40e^{x}
limit as x approaches 12 of sqrt(x-3)	\lim\:_{x\to\:12}(\sqrt{x-3})
tangent of f(x)=x^2-3,\at x=-2	tangent\:f(x)=x^{2}-3,\at\:x=-2
integral of x/(sqrt(2x^2+5))	\int\:\frac{x}{\sqrt{2x^{2}+5}}dx
integral of (3x+1)/(x^2+x-6)	\int\:\frac{3x+1}{x^{2}+x-6}dx
area x=7y^2,x=3+4y^2	area\:x=7y^{2},x=3+4y^{2}
integral of sin(mpix)	\int\:\sin(mπx)dx
derivative of f(x)=2x-(e^x)/2	derivative\:f(x)=2x-\frac{e^{x}}{2}
integral from pi to infinity of 4/(x^2)	\int\:_{π}^{\infty\:}\frac{4}{x^{2}}dx
y^{''}+2y^'+y=(3x+4)e^{3x}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=(3x+4)e^{3x}
f(x)=x^5-x^3+3	f(x)=x^{5}-x^{3}+3
normal of y=x^4+9e^x,(0,9)	normal\:y=x^{4}+9e^{x},(0,9)
derivative of 9xe^{-kx}	derivative\:9xe^{-kx}
area y=4-x^2,y=14-7x	area\:y=4-x^{2},y=14-7x
integral of 8cos(x)+3x-8	\int\:8\cos(x)+3x-8dx
derivative of y=ln(1/((x-2)^3))	derivative\:y=\ln(\frac{1}{(x-2)^{3}})
laplacetransform-5e^{4t}	laplacetransform\:-5e^{4t}
(\partial)/(\partial x)(xsin(2x^2y))	\frac{\partial\:}{\partial\:x}(x\sin(2x^{2}y))
integral of 1/(tsqrt(4t^2-1))	\int\:\frac{1}{t\sqrt{4t^{2}-1}}dt
y^{''}-y=x^2e^x	y^{\prime\:\prime\:}-y=x^{2}e^{x}
integral of 2(x-1)	\int\:2(x-1)dx
y^{''}+2y^'+36y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+36y=0,y(0)=1,y^{\prime\:}(0)=0
integral from 1 to 3 of (x-1)	\int\:_{1}^{3}(x-1)dx
derivative of 2tan(xsec^2(x))	\frac{d}{dx}(2\tan(x)\sec^{2}(x))
derivative of ln(tan(x))	derivative\:\ln(\tan(x))
(\partial)/(\partial x)(((-x+y))/(xy+3x))	\frac{\partial\:}{\partial\:x}(\frac{(-x+y)}{x\cdot\:y+3\cdot\:x})
y^'=y^2(5+x)	y^{\prime\:}=y^{2}(5+x)
(\partial)/(\partial x)(z/(1+z^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{z}{1+z^{2}y^{2}})
derivative of Axe^{3x}	\frac{d}{dx}(Axe^{3x})
f(t)=sin(t)-tcos(t)	f(t)=\sin(t)-t\cos(t)
f^'(x)=(1-e^x)/(9+e^x)	f^{\prime\:}(x)=\frac{1-e^{x}}{9+e^{x}}
xy^'+y=-2xy^2,y(1)=2	xy^{\prime\:}+y=-2xy^{2},y(1)=2
(\partial)/(\partial y)(y^2sin(xy))	\frac{\partial\:}{\partial\:y}(y^{2}\sin(xy))
limit as x approaches 5 of 2/((x-5)^6)	\lim\:_{x\to\:5}(\frac{2}{(x-5)^{6}})
limit as x approaches 1 of 2x^{-1}	\lim\:_{x\to\:1}(2x^{-1})
laplacetransform te^{-5t}sin(5t)	laplacetransform\:te^{-5t}\sin(5t)
integral of 6e^7	\int\:6e^{7}dx
derivative of e^{2x}+3	\frac{d}{dx}(e^{2x}+3)
y^{''}+5y^'+6y=e-3x	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=e-3x
integral of (e^{2t})/(e^t+3)	\int\:\frac{e^{2t}}{e^{t}+3}dt
(dy)/(dx)+6y=4	\frac{dy}{dx}+6y=4
laplacetransform 2cos(2t)	laplacetransform\:2\cos(2t)
derivative of e^{y-1}	derivative\:e^{y-1}
limit as x approaches 2-of (\|x-2\|)/x	\lim\:_{x\to\:2-}(\frac{\left\|x-2\right\|}{x})
(dy}{dx}=x+\frac{3y)/x	\frac{dy}{dx}=x+\frac{3y}{x}
(\partial)/(\partial x)(1/y-1/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{y}-\frac{1}{x^{2}})
(\partial)/(\partial y)(5x^2y^2)	\frac{\partial\:}{\partial\:y}(5x^{2}y^{2})
xdy-(2xe^{(-y)/x}+y)dx=0	xdy-(2xe^{\frac{-y}{x}}+y)dx=0
d/(dθ)(8cos(θ)+2sin(θ))	\frac{d}{dθ}(8\cos(θ)+2\sin(θ))
(dy)/(dx)-xe^y=2e^y	\frac{dy}{dx}-xe^{y}=2e^{y}
(d^2y)/(dx^2)+2(dy)/(dx)+y=e^{-x}*ln(x)	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+y=e^{-x}\cdot\:\ln(x)
(\partial)/(\partial x)(1+xy^2)	\frac{\partial\:}{\partial\:x}(1+xy^{2})
limit as h approaches 0 of 3/h	\lim\:_{h\to\:0}(\frac{3}{h})
derivative of 4tan^2(7x)	derivative\:4\tan^{2}(7x)
(dy)/(dx)=-1/2 y	\frac{dy}{dx}=-\frac{1}{2}y
derivative of f(x)=((x^2-1))/(x^2+1)	derivative\:f(x)=\frac{(x^{2}-1)}{x^{2}+1}
integral of 5x^2+(2/x)^4	\int\:5x^{2}+(\frac{2}{x})^{4}dx
(d^2y)/(dx^2)+y=0	\frac{d^{2}y}{dx^{2}}+y=0
y^'-1/x y=x^2e^x	y^{\prime\:}-\frac{1}{x}y=x^{2}e^{x}
derivative of (cos(2x)/(sin(3x)))	\frac{d}{dx}(\frac{\cos(2x)}{\sin(3x)})
integral from 0 to 16 of sqrt(t^2+2t+1)	\int\:_{0}^{16}\sqrt{t^{2}+2t+1}dt
y^'=((x^3y^3+4x^3))/(y^2)	y^{\prime\:}=\frac{(x^{3}y^{3}+4x^{3})}{y^{2}}
integral from 1/5 to 3 of 12xln(5x)	\int\:_{\frac{1}{5}}^{3}12x\ln(5x)dx
integral of (x^2+sqrt(x)+1/x)	\int\:(x^{2}+\sqrt{x}+\frac{1}{x})dx
derivative of f(x)=5x^2-5x+9	derivative\:f(x)=5x^{2}-5x+9
derivative of-9x^3+27x+7x-66	\frac{d}{dx}(-9x^{3}+27x+7x-66)
tangent of 3sqrt(x),\at x=4	tangent\:3\sqrt{x},\at\:x=4
integral of 5tan^3(x)sec^3(x)	\int\:5\tan^{3}(x)\sec^{3}(x)dx
integral from 1 to 4 of 1/(sqrt(x))	\int\:_{1}^{4}\frac{1}{\sqrt{x}}dx
(\partial)/(\partial x)(arcsin(xyz))	\frac{\partial\:}{\partial\:x}(\arcsin(xyz))
integral of (x^3)/((5-x^4)^6)	\int\:\frac{x^{3}}{(5-x^{4})^{6}}dx
(dy)/(dx)=-xy	\frac{dy}{dx}=-xy
integral from 0 to 2pi of cos^2(6x)	\int\:_{0}^{2π}\cos^{2}(6x)dx

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