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Popular Calculus Problems

integral of (2x+1)/(x^2+5x+6)	\int\:\frac{2x+1}{x^{2}+5x+6}dx
derivative of sqrt(2x^2+5)	\frac{d}{dx}(\sqrt{2x^{2}+5})
integral of 4x^2e^{3x}	\int\:4x^{2}e^{3x}dx
y^{''}+y=3e^{-4x}	y^{\prime\:\prime\:}+y=3e^{-4x}
integral of (3ln^2(x))/(x^2)	\int\:\frac{3\ln^{2}(x)}{x^{2}}dx
derivative of (xsec(-(y/x+y))/x)	\frac{d}{dx}(\frac{x\sec(-(\frac{y}{x})+y)}{x})
integral of (x^2-1)^3	\int\:(x^{2}-1)^{3}dx
integral of sin(t^4)	\int\:\sin(t^{4})dt
f(t)=1+t	f(t)=1+t
derivative of {y}(x)	\frac{d}{dx}({y}(x))
y^'+(ty)/(t^2)= 4/(t^2)	y^{\prime\:}+\frac{ty}{t^{2}}=\frac{4}{t^{2}}
(dy)/(dx)= x/(7cos(y))	\frac{dy}{dx}=\frac{x}{7\cos(y)}
derivative of ((x+3^2)/((x+2)^5(x+4)^7))	\frac{d}{dx}(\frac{(x+3)^{2}}{(x+2)^{5}(x+4)^{7}})
integral of cotan^2(x)	\int\:co\tan^{2}(x)dx
(\partial)/(\partial x)(1/(2-x+y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2-x+y})
tangent of 2sqrt(x)+x^2-5,\at x=1	tangent\:2\sqrt{x}+x^{2}-5,\at\:x=1
normal of y= x/(sqrt(4+x^2)),(0,0)	normal\:y=\frac{x}{\sqrt{4+x^{2}}},(0,0)
integral of (sqrt(x^2-8))/(x^4)	\int\:\frac{\sqrt{x^{2}-8}}{x^{4}}dx
integral from 0 to 1 of (x^3-3x^2)	\int\:_{0}^{1}(x^{3}-3x^{2})dx
d/(dt)(4t)	\frac{d}{dt}(4t)
integral from 0 to infinity of e^{-kx}	\int\:_{0}^{\infty\:}e^{-kx}dx
(2x-1)dx+(7y+4)dy=0	(2x-1)dx+(7y+4)dy=0
integral of (3x^2+4x+5)/(sqrt(x))	\int\:\frac{3x^{2}+4x+5}{\sqrt{x}}dx
integral of 40arctan(sqrt(x))	\int\:40\arctan(\sqrt{x})dx
(\partial)/(\partial y)(16-4x^2-y^2)	\frac{\partial\:}{\partial\:y}(16-4x^{2}-y^{2})
integral of sec^2(5t)	\int\:\sec^{2}(5t)dt
derivative of g(x)=x^2(1-5x)	derivative\:g(x)=x^{2}(1-5x)
f(x)=(2x^2-1)/(x^3-x)	f(x)=\frac{2x^{2}-1}{x^{3}-x}
(\partial)/(\partial x)(2z^3-3(x^2+y^2)z)	\frac{\partial\:}{\partial\:x}(2z^{3}-3(x^{2}+y^{2})z)
limit as x approaches-8+of x/(x+8)	\lim\:_{x\to\:-8+}(\frac{x}{x+8})
(\partial)/(\partial x)(6x^3y+6y^5+1)	\frac{\partial\:}{\partial\:x}(6x^{3}y+6y^{5}+1)
d/(dv)(sqrt(v-1))	\frac{d}{dv}(\sqrt{v-1})
integral from 1 to R of x^{-7/5}	\int\:_{1}^{R}x^{-\frac{7}{5}}dx
derivative of (6x^5-4x^4+7x(x^3-x^2-1))	\frac{d}{dx}((6x^{5}-4x^{4}+7x)(x^{3}-x^{2}-1))
(\partial)/(\partial x)(e^{x+y+5})	\frac{\partial\:}{\partial\:x}(e^{x+y+5})
(\partial)/(\partial z)((x-y)/(x+z))	\frac{\partial\:}{\partial\:z}(\frac{x-y}{x+z})
y^{''}-2y^'+y=(e^t)/(1+t^2)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{e^{t}}{1+t^{2}}
integral from 0 to pi of sin^4(3x)	\int\:_{0}^{π}\sin^{4}(3x)dx
integral of-1	\int\:-1dx
(\partial)/(\partial x)(cos(2x-3y))	\frac{\partial\:}{\partial\:x}(\cos(2x-3y))
integral of cos(x)*sin(2x)	\int\:\cos(x)\cdot\:\sin(2x)dx
(\partial)/(\partial x)(cos(2xy))	\frac{\partial\:}{\partial\:x}(\cos(2xy))
3x^2ydx+x^3dy=0	3x^{2}ydx+x^{3}dy=0
integral from 0 to 2 of e^{6x}	\int\:_{0}^{2}e^{6x}dx
integral of-cos(5x)	\int\:-\cos(5x)dx
simplify (x^2+x)/(x^2+4x)	simplify\:\frac{x^{2}+x}{x^{2}+4x}
(dy)/(dx)=((2x(y-1))/(x^2+3)),y(1)=9	\frac{dy}{dx}=(\frac{2x(y-1)}{x^{2}+3}),y(1)=9
(d^2)/(dx^2)(x^4)	\frac{d^{2}}{dx^{2}}(x^{4})
(x+2y)dy=dx	(x+2y)dy=dx
derivative of x*e^{1/x}	\frac{d}{dx}(x\cdot\:e^{\frac{1}{x}})
limit as x approaches 1 of x(1)	\lim\:_{x\to\:1}(x(1))
integral from 4 to 8 of 2/(x^3)	\int\:_{4}^{8}\frac{2}{x^{3}}dx
integral of 1/(sqrt(24x+6x^2))	\int\:\frac{1}{\sqrt{24x+6x^{2}}}dx
integral of 7/(sqrt(7x^2+14x+5))	\int\:\frac{7}{\sqrt{7x^{2}+14x+5}}dx
limit as x approaches 0 of 1/x	\lim\:_{x\to\:0}(\frac{1}{x})
derivative of f(x)=(tan(x)-1)/(sec(x))	derivative\:f(x)=\frac{\tan(x)-1}{\sec(x)}
(\partial)/(\partial y)(e^y*cos(x))	\frac{\partial\:}{\partial\:y}(e^{y}\cdot\:\cos(x))
inverse oflaplace ((s+3))/(s^2+2s+1)	inverselaplace\:\frac{(s+3)}{s^{2}+2s+1}
4y^{''}-16y^'+18y=0	4y^{\prime\:\prime\:}-16y^{\prime\:}+18y=0
derivative of (25x^2-1/(x+3))	\frac{d}{dx}(\frac{25x^{2}-1}{x+3})
integral from 0 to 1 of (e^{-0.1x})	\int\:_{0}^{1}(e^{-0.1x})dx
derivative of (x+2^3)	\frac{d}{dx}((x+2)^{3})
limit as z approaches 0 of z^3e^{1/z}	\lim\:_{z\to\:0}(z^{3}e^{\frac{1}{z}})
integral from 1 to 2 of (e^{3/x})/(x^2)	\int\:_{1}^{2}\frac{e^{\frac{3}{x}}}{x^{2}}dx
y^{''}+16y^'+64y=0	y^{\prime\:\prime\:}+16y^{\prime\:}+64y=0
integral from-2 to 2 of x^3+1	\int\:_{-2}^{2}x^{3}+1dx
tangent of f(x)=x^3+x,\at x=0	tangent\:f(x)=x^{3}+x,\at\:x=0
laplacetransform cos^2(ax)	laplacetransform\:\cos^{2}(ax)
f^'(s)=10s-12s^3,f(3)=2	f^{\prime\:}(s)=10s-12s^{3},f(3)=2
sum from n=0 to infinity of x^{2n}	\sum\:_{n=0}^{\infty\:}x^{2n}
slope of y=x^2+1,(2,5)	slope\:y=x^{2}+1,(2,5)
d/(dt)(e^{7t})	\frac{d}{dt}(e^{7t})
integral of 1/((x+5)sqrt(10x+x^2))	\int\:\frac{1}{(x+5)\sqrt{10x+x^{2}}}dx
integral of 9-x^2	\int\:9-x^{2}dx
taylor-1/x 2	taylor\:-\frac{1}{x}2
derivative of y= x/(sqrt(x^2+1))	derivative\:y=\frac{x}{\sqrt{x^{2}+1}}
simplify 3x^2-1/x	simplify\:3x^{2}-\frac{1}{x}
tangent of f(x)=x^2+2x,\at x=34	tangent\:f(x)=x^{2}+2x,\at\:x=34
limit as x approaches infinity of 2^x	\lim\:_{x\to\:\infty\:}(2^{x})
integral of (x^2+2x-1)/((x+1)(x+2)(x+3))	\int\:\frac{x^{2}+2x-1}{(x+1)(x+2)(x+3)}dx
derivative of f(x)=(4x-9)^2	derivative\:f(x)=(4x-9)^{2}
y^'-y=x,y(0)=1	y^{\prime\:}-y=x,y(0)=1
limit as x approaches-2 of x^3+8	\lim\:_{x\to\:-2}(x^{3}+8)
integral of x(x-1)^4	\int\:x(x-1)^{4}dx
derivative of f(x)=4^{x^9}	derivative\:f(x)=4^{x^{9}}
derivative of log_{e}(sqrt(x))	\frac{d}{dx}(\log_{e}(\sqrt{x}))
integral of 9/(x^2sqrt(x^2+16))	\int\:\frac{9}{x^{2}\sqrt{x^{2}+16}}dx
derivative of tan^2(5θ)	derivative\:\tan^{2}(5θ)
sum from n=1 to infinity of 5(-1)^nnx^n	\sum\:_{n=1}^{\infty\:}5(-1)^{n}nx^{n}
laplacetransform e^{-4}	laplacetransform\:e^{-4}
derivative of (sin(x^2+1)^{1/({f)(x)}})	\frac{d}{dx}((\sin(x^{2})+1)^{\frac{1}{{f}(x)}})
integral of x^2sqrt(x^2+1)	\int\:x^{2}\sqrt{x^{2}+1}dx
normal of-x^3+2x^2-2,\at x=1	normal\:-x^{3}+2x^{2}-2,\at\:x=1
integral of-x^5e^x	\int\:-x^{5}e^{x}dx
(\partial)/(\partial x)(4yx^3-6y^2x^2)	\frac{\partial\:}{\partial\:x}(4yx^{3}-6y^{2}x^{2})
tangent of f(x)= 1/(1+x^2),(1, 1/2)	tangent\:f(x)=\frac{1}{1+x^{2}},(1,\frac{1}{2})
d/(dy)(4)	\frac{d}{dy}(4)
integral of 15z^3e^z	\int\:15z^{3}e^{z}dz
inverse oflaplace e^{-4(t-1)}	inverselaplace\:e^{-4(t-1)}
y^{'''}+4y^'=cot(2x)	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:}=\cot(2x)

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