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Popular Calculus Problems

integral of (x^2-9)	\int\:(x^{2}-9)dx
integral of (x(x-6))/((x-3)^3)	\int\:\frac{x(x-6)}{(x-3)^{3}}dx
integral of 3/(9-4x^2)	\int\:\frac{3}{9-4x^{2}}dx
y^{''}-y^'-6y=-4e^{2t},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-y^{\prime\:}-6y=-4e^{2t},y(0)=0,y^{\prime\:}(0)=0
derivative of f(x)=(2-x^2)/(2+x^2)	derivative\:f(x)=\frac{2-x^{2}}{2+x^{2}}
derivative of f(sqrt(x))	derivative\:f(\sqrt{x})
slope ofintercept (-5,5),(5,-5)	slopeintercept\:(-5,5),(5,-5)
(ln(3))^'	(\ln(3))^{\prime\:}
(\partial)/(\partial x)(z+1-xe^ycos(z))	\frac{\partial\:}{\partial\:x}(z+1-xe^{y}\cos(z))
derivative of y=(arctan(3x))^2	derivative\:y=(\arctan(3x))^{2}
y^{''}+9y^'=5csc^2(3t)	y^{\prime\:\prime\:}+9y^{\prime\:}=5\csc^{2}(3t)
(\partial)/(\partial x)(ycos(x-y)-z)	\frac{\partial\:}{\partial\:x}(y\cos(x-y)-z)
integral of (x^4(5-x^2))	\int\:(x^{4}(5-x^{2}))dx
limit as x approaches 1000 of 18pi^2	\lim\:_{x\to\:1000}(18π^{2})
(\partial)/(\partial x)(x(2x-y^3))	\frac{\partial\:}{\partial\:x}(x(2x-y^{3}))
tangent of y=sqrt(5x+6),(2,4)	tangent\:y=\sqrt{5x+6},(2,4)
integral of (x+3)^2sin(x)	\int\:(x+3)^{2}\sin(x)dx
derivative of sin(-4x)	\frac{d}{dx}(\sin(-4x))
(x^2+1)(dy)/(dx)+4xy=x	(x^{2}+1)\frac{dy}{dx}+4xy=x
derivative of ((sqrt(x)))/(x+1)	derivative\:\frac{(\sqrt{x})}{x+1}
integral of x/(x^4+8x^2+17)	\int\:\frac{x}{x^{4}+8x^{2}+17}dx
(\partial)/(\partial x)(ycos(x))	\frac{\partial\:}{\partial\:x}(y\cos(x))
integral from 5 to e^3 of 1/x	\int\:_{5}^{e^{3}}\frac{1}{x}dx
y^'=xe^y	y^{\prime\:}=xe^{y}
(\partial)/(\partial y)(sin^2(y))	\frac{\partial\:}{\partial\:y}(\sin^{2}(y))
(\partial)/(\partial x)(x^{e^x})	\frac{\partial\:}{\partial\:x}(x^{e^{x}})
slope of (-4)(12.2)	slope\:(-4)(12.2)
(\partial)/(\partial x)((x^9)(y^6)+7(x^5)y)	\frac{\partial\:}{\partial\:x}((x^{9})(y^{6})+7(x^{5})y)
integral of (2x^2-4x+4)/(sqrt(3+2x-x^2))	\int\:\frac{2x^{2}-4x+4}{\sqrt{3+2x-x^{2}}}dx
y^'=y-y^2	y^{\prime\:}=y-y^{2}
(dy)/(dx)=10-y	\frac{dy}{dx}=10-y
limit as x approaches-5+of (x+10)/(x+5)	\lim\:_{x\to\:-5+}(\frac{x+10}{x+5})
integral of x^2e^{16x}	\int\:x^{2}e^{16x}dx
derivative of (e^x-e^{-x}/(e^x+e^{-x)})	\frac{d}{dx}(\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}})
join 3/2 sin(x)	join\:\frac{3}{2}\sin(x)
area 1/x ,1,5	area\:\frac{1}{x},1,5
integral of (sqrt(2y))	\int\:(\sqrt{2y})dy
derivative of y=(1/3)^x	derivative\:y=(\frac{1}{3})^{x}
integral of-4ln(x^2-1)	\int\:-4\ln(x^{2}-1)dx
sum from n=1 to infinity of n(1)^n	\sum\:_{n=1}^{\infty\:}n(1)^{n}
tangent of 7x^2+8x	tangent\:7x^{2}+8x
integral of (x^2)/(sqrt(x^2+4x-12))	\int\:\frac{x^{2}}{\sqrt{x^{2}+4x-12}}dx
integral of (8x^3+1/(2x^2))	\int\:(8x^{3}+\frac{1}{2x^{2}})dx
inverse oflaplace ((3s-4))/(s^2+9)	inverselaplace\:\frac{(3s-4)}{s^{2}+9}
integral from 0 to 9 of 2sqrt(y)	\int\:_{0}^{9}2\sqrt{y}dy
d/(dθ)(sec(θ)tan(θ))	\frac{d}{dθ}(\sec(θ)\tan(θ))
inverse oflaplace 3/(s-9)	inverselaplace\:\frac{3}{s-9}
derivative of {f}(x{g}(x))	\frac{d}{dx}({f}(x){g}(x))
derivative of y/(y+a/y)	derivative\:\frac{y}{y+\frac{a}{y}}
sum from n=0 to infinity of n/(e^{2n)}	\sum\:_{n=0}^{\infty\:}\frac{n}{e^{2n}}
integral of (e^{4x}-e^{2x}+1)/(e^x)	\int\:\frac{e^{4x}-e^{2x}+1}{e^{x}}dx
y^'=y	y^{\prime\:}=y
derivative of f(x)=4sqrt(x)-6	derivative\:f(x)=4\sqrt{x}-6
parity tan(sec(cos(t)))	parity\:\tan(\sec(\cos(t)))
derivative of x^0	\frac{d}{dx}(x^{0})
limit as x approaches 5 of 4x^3-6x^2	\lim\:_{x\to\:5}(4x^{3}-6x^{2})
limit as x approaches-5 of (2x+3)/(3x+2)	\lim\:_{x\to\:-5}(\frac{2x+3}{3x+2})
integral of 1/(sqrt(60x+10x^2))	\int\:\frac{1}{\sqrt{60x+10x^{2}}}dx
(dy)/(dx)+y^2sin(x)=0	\frac{dy}{dx}+y^{2}\sin(x)=0
integral of (x^2)/(sqrt(1+x^6))	\int\:\frac{x^{2}}{\sqrt{1+x^{6}}}dx
integral of 7/(((x-1)sqrt(x^2-2x-48)))	\int\:\frac{7}{((x-1)\sqrt{x^{2}-2x-48})}dx
y^'=3y+t	y^{\prime\:}=3y+t
derivative of 1/pi sin(pix)	derivative\:\frac{1}{π}\sin(πx)
derivative of 3/(x+5)	\frac{d}{dx}(\frac{3}{x+5})
integral of x^4cos(x)	\int\:x^{4}\cos(x)dx
derivative of 5/((3x^2-x)^4)	derivative\:\frac{5}{(3x^{2}-x)^{4}}
derivative of 1/(x-a)	\frac{d}{dx}(\frac{1}{x-a})
maclaurin (1-e^{-ax})^2	maclaurin\:(1-e^{-ax})^{2}
inverse oflaplace (3e^{(-2s)})/((s^2-4s+3))	inverselaplace\:\frac{3e^{(-2s)}}{(s^{2}-4s+3)}
derivative of ln(100sin^2(x))	derivative\:\ln(100\sin^{2}(x))
derivative of f(x)=(4x^2tan(x))/(sec(x))	derivative\:f(x)=\frac{4x^{2}\tan(x)}{\sec(x)}
limit as x approaches-2 of-0.8	\lim\:_{x\to\:-2}(-0.8)
xdy-ydx=(2x^2-3)dx	xdy-ydx=(2x^{2}-3)dx
taylor 3/(x^2-x-2)	taylor\:\frac{3}{x^{2}-x-2}
integral from 1 to 3 of ln(2x)	\int\:_{1}^{3}\ln(2x)dx
limit as x approaches pi of 5	\lim\:_{x\to\:π}(5)
derivative of f(x)=sqrt(x)sec(x)	derivative\:f(x)=\sqrt{x}\sec(x)
derivative of x^2sqrt(x-4)	\frac{d}{dx}(x^{2}\sqrt{x-4})
taylor cos(x)	taylor\:\cos(x)
limit as x approaches 0 of x^2-sin(1/x)	\lim\:_{x\to\:0}(x^{2}-\sin(\frac{1}{x}))
derivative of y=x^3(2x+3)^7	derivative\:y=x^{3}(2x+3)^{7}
area 3x, 3/x ,x=3	area\:3x,\frac{3}{x},x=3
(dy)/(dx)=-y/x	\frac{dy}{dx}=-\frac{y}{x}
limit as x approaches 0 of cos(pi)	\lim\:_{x\to\:0}(\cos(π))
area x+y=10,(2,8)	area\:x+y=10,(2,8)
integral of (2x^3+x-1)/(x^3+x^2-4x-4)	\int\:\frac{2x^{3}+x-1}{x^{3}+x^{2}-4x-4}dx
integral of (16x+3)sqrt(8x^2+3x)	\int\:(16x+3)\sqrt{8x^{2}+3x}dx
derivative of (x-2(2x+3))	\frac{d}{dx}((x-2)(2x+3))
tangent of y=(5x)/(1+x^2),(4, 20/17)	tangent\:y=\frac{5x}{1+x^{2}},(4,\frac{20}{17})
integral of (7-98x)/(sqrt(81-49x^2))	\int\:\frac{7-98x}{\sqrt{81-49x^{2}}}dx
derivative of y=x^{0.4}	derivative\:y=x^{0.4}
derivative of (x+1^3(x-2))	\frac{d}{dx}((x+1)^{3}(x-2))
derivative of 9x+5	\frac{d}{dx}(9x+5)
integral of sec(32x)tan(32x)	\int\:\sec(32x)\tan(32x)dx
derivative of 1/(x+2)	derivative\:\frac{1}{x+2}
integral of (7t^3+t^2)/(sqrt(t))	\int\:\frac{7t^{3}+t^{2}}{\sqrt{t}}dt
derivative of 2^{8-x^2}	derivative\:2^{8-x^{2}}
integral of 1/(4x^2+2)	\int\:\frac{1}{4x^{2}+2}dx
sum from n=0 to infinity of ((n^n))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(n^{n})}{n!}
integral of 1/z	\int\:\frac{1}{z}dz

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