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Popular Calculus Problems

integral of 1/(5x-6)	\int\:\frac{1}{5x-6}dx
limit as x approaches 0 of xcot(2x)	\lim\:_{x\to\:0}(x\cot(2x))
integral from 0 to 25 of 4/5 x	\int\:_{0}^{25}\frac{4}{5}xdx
y^'+y=5*x+1	y^{\prime\:}+y=5\cdot\:x+1
(\partial)/(\partial z)(xy^2z)	\frac{\partial\:}{\partial\:z}(xy^{2}z)
y^{''}+8y^'+4y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+4y=0
derivative of f(x)=(x^2)/(x^2+7)	derivative\:f(x)=\frac{x^{2}}{x^{2}+7}
integral of-(ln(x))/2	\int\:-\frac{\ln(x)}{2}dx
u'(t)	u\prime\:(t)
(\partial)/(\partial y)(arctan(x-y))	\frac{\partial\:}{\partial\:y}(\arctan(x-y))
limit as x approaches infinity+of 0	\lim\:_{x\to\:\infty\:+}(0)
integral of sec^2(2x+1)	\int\:\sec^{2}(2x+1)dx
(\partial)/(\partial x)(2x-5)	\frac{\partial\:}{\partial\:x}(2x-5)
(\partial)/(\partial x)((u-v)/(u+v))	\frac{\partial\:}{\partial\:x}(\frac{u-v}{u+v})
integral of 6xarccos(6x)	\int\:6x\arccos(6x)dx
integral of t^2sin(3t)	\int\:t^{2}\sin(3t)dt
integral of e^xx^3	\int\:e^{x}x^{3}dx
integral from 3 to 6 of 1/(sqrt(3x+7))	\int\:_{3}^{6}\frac{1}{\sqrt{3x+7}}dx
derivative of (3x^4(4x^3+4x))	\frac{d}{dx}((3x^{4})(4x^{3}+4x))
integral of (e^{2x})/(e^x-5)	\int\:\frac{e^{2x}}{e^{x}-5}dx
derivative of f(x)=(7x^2-12x)e^x	derivative\:f(x)=(7x^{2}-12x)e^{x}
area 3x^2,x^2+6	area\:3x^{2},x^{2}+6
(dy)/(dx)=6xy	\frac{dy}{dx}=6xy
derivative of 2e^x	derivative\:2e^{x}
integral from 0 to 1 of 2+sqrt(2+x^2)	\int\:_{0}^{1}2+\sqrt{2+x^{2}}dx
integral of-40	\int\:-40
derivative of (sin(4x)/(2+cos(4x)))	\frac{d}{dx}(\frac{\sin(4x)}{2+\cos(4x)})
integral of 4e^{5x+e^{5x}}	\int\:4e^{5x+e^{5x}}dx
(dy)/(dx)=(x^2-y^2)/(3xy)	\frac{dy}{dx}=\frac{x^{2}-y^{2}}{3xy}
derivative of log_{2}(3x^2)	\frac{d}{dx}(\log_{2}(3x^{2}))
integral of sqrt(33+8x-x^2)	\int\:\sqrt{33+8x-x^{2}}dx
integral of 12cos^4(2x)sin^3(2x)	\int\:12\cos^{4}(2x)\sin^{3}(2x)dx
derivative of x^2-4x-4	derivative\:x^{2}-4x-4
derivative of 9sqrt(x)sin(x)	derivative\:9\sqrt{x}\sin(x)
derivative of (2sin(x)/(1+cos(x)))	\frac{d}{dx}(\frac{2\sin(x)}{1+\cos(x)})
integral of 2^{3x+log_{2}(x)}	\int\:2^{3x+\log_{2}(x)}dx
derivative of-0.1x^2+0.8x+9	derivative\:-0.1x^{2}+0.8x+9
integral of (e^{arctan(x)})/(x^2+1)	\int\:\frac{e^{\arctan(x)}}{x^{2}+1}dx
integral of (3-4x)/(sqrt(16-9x^2))	\int\:\frac{3-4x}{\sqrt{16-9x^{2}}}dx
derivative of f(x)=sqrt((x-1)/(x+1))	derivative\:f(x)=\sqrt{\frac{x-1}{x+1}}
integral of e^x*arctan(e^x)	\int\:e^{x}\cdot\:\arctan(e^{x})dx
tangent of f(x)=x^2-4,(5,21)	tangent\:f(x)=x^{2}-4,(5,21)
integral of (e^{7x}-1/(sqrt(x)))	\int\:(e^{7x}-\frac{1}{\sqrt{x}})dx
integral of (4x-6)/(x^2-2x)	\int\:\frac{4x-6}{x^{2}-2x}dx
(d^2)/(dx^2)(e^{x^2})	\frac{d^{2}}{dx^{2}}(e^{x^{2}})
integral of x*e^{-4x}	\int\:x\cdot\:e^{-4x}dx
d/(dy)(x^{8y})	\frac{d}{dy}(x^{8y})
integral of 2pixsin(x^2)	\int\:2πx\sin(x^{2})dx
implicit (dy)/(dx),x^{1/2}+y^{1/2}=9	implicit\:\frac{dy}{dx},x^{\frac{1}{2}}+y^{\frac{1}{2}}=9
integral of (arcsin^3(x))/(sqrt(1-x^2))	\int\:\frac{\arcsin^{3}(x)}{\sqrt{1-x^{2}}}dx
derivative of (8x^2-14xe^x)	\frac{d}{dx}((8x^{2}-14x)e^{x})
integral of t^2+1	\int\:t^{2}+1dt
derivative of sqrt(x-2y)	\frac{d}{dx}(\sqrt{x-2y})
tangent of f(x)=x^2-2x-8,\at x=-2	tangent\:f(x)=x^{2}-2x-8,\at\:x=-2
area y=((3x+1))/2 ,y=x^2-2	area\:y=\frac{(3x+1)}{2},y=x^{2}-2
xy(dy)/(dx)+y^2=32x	xy\frac{dy}{dx}+y^{2}=32x
integral of x/(sqrt(4-x^2))	\int\:\frac{x}{\sqrt{4-x^{2}}}dx
integral of sqrt(2x+9)	\int\:\sqrt{2x+9}dx
2ty^'-3y=0	2ty^{\prime\:}-3y=0
tangent of f(x)= 7/(x^4),\at x=-3	tangent\:f(x)=\frac{7}{x^{4}},\at\:x=-3
tangent of y=sqrt(x+2),(-1,1)	tangent\:y=\sqrt{x+2},(-1,1)
(dy)/(dx)=(y^2+xy+x^2)/(x^2),y(1)=-1	\frac{dy}{dx}=\frac{y^{2}+xy+x^{2}}{x^{2}},y(1)=-1
limit as x approaches-4+of (-2)/(x^2-16)	\lim\:_{x\to\:-4+}(\frac{-2}{x^{2}-16})
(\partial)/(\partial x)(ln(x/4))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{4}))
integral of (32x^2)/((x-12)(x+4)^2)	\int\:\frac{32x^{2}}{(x-12)(x+4)^{2}}dx
derivative of (x^4)/(5-x^3)	derivative\:\frac{x^{4}}{5-x^{3}}
integral from 0 to 1/2 of (e^x)(e^x)	\int\:_{0}^{\frac{1}{2}}(e^{x})(e^{x})dx
integral of 2/(2+cos(x))	\int\:\frac{2}{2+\cos(x)}dx
integral of 1/(s^2+1)	\int\:\frac{1}{s^{2}+1}ds
integral of x+e^{2x}	\int\:x+e^{2x}dx
(\partial)/(\partial x)(e^{9x+5y})	\frac{\partial\:}{\partial\:x}(e^{9x+5y})
derivative of (2x^2+1/((1-x^2)^{5/2)})	\frac{d}{dx}(\frac{2x^{2}+1}{(1-x^{2})^{\frac{5}{2}}})
integral of 1/(2*sqrt(tan(x)))	\int\:\frac{1}{2\cdot\:\sqrt{\tan(x)}}dx
integral of x/(x+\sqrt[3]{x)}	\int\:\frac{x}{x+\sqrt[3]{x}}dx
derivative of (1/(x^2-9/(x^4))(x+5x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{9}{x^{4}})(x+5x^{3}))
limit as x approaches 0 of 2e^{3x}	\lim\:_{x\to\:0}(2e^{3x})
tangent of f(x)=(12x)/(x^2-4),(4,4)	tangent\:f(x)=\frac{12x}{x^{2}-4},(4,4)
integral of 2/(x^2sqrt(1+x^2))	\int\:\frac{2}{x^{2}\sqrt{1+x^{2}}}dx
derivative of (8x^2+9)/(x^2+5)	derivative\:\frac{8x^{2}+9}{x^{2}+5}
laplacetransform 45	laplacetransform\:45
derivative of 3/(x^9)	derivative\:\frac{3}{x^{9}}
y^'=7x+y,y(0)=9	y^{\prime\:}=7x+y,y(0)=9
integral of 3x^2-12	\int\:3x^{2}-12dx
integral of x^9sqrt(x^5+2)	\int\:x^{9}\sqrt{x^{5}+2}dx
xy^'-y^2ln(x)+y=0	xy^{\prime\:}-y^{2}\ln(x)+y=0
limit as x approaches 3 of 7x-6	\lim\:_{x\to\:3}(7x-6)
derivative of sin(x)	derivative\:\sin(x)
(\partial)/(\partial x)(1000-4xy+xy^2)	\frac{\partial\:}{\partial\:x}(1000-4xy+xy^{2})
(dy)/(dx)=(2x)/((1+x^2))	\frac{dy}{dx}=\frac{2x}{(1+x^{2})}
(\partial)/(\partial y)(e^{2x}cos(3y))	\frac{\partial\:}{\partial\:y}(e^{2x}\cos(3y))
tangent of y= 5/(4x+1)	tangent\:y=\frac{5}{4x+1}
derivative of (3-17x^2/(3x^3))	\frac{d}{dx}(\frac{3-17x^{2}}{3x^{3}})
derivative of 5e^xtan(x)	derivative\:5e^{x}\tan(x)
integral of (4x^2+3x-1)/(x^3-x^2)	\int\:\frac{4x^{2}+3x-1}{x^{3}-x^{2}}dx
(\partial)/(\partial y)(y/(x+z))	\frac{\partial\:}{\partial\:y}(\frac{y}{x+z})
integral of (2x+1)/(x+1)	\int\:\frac{2x+1}{x+1}dx
tangent of f(x)= 3/(x^2)	tangent\:f(x)=\frac{3}{x^{2}}
(\partial)/(\partial x)(((a+cx))/(c+b))	\frac{\partial\:}{\partial\:x}(\frac{(a+cx)}{c+b})
integral of cos(θ)sin(θ)	\int\:\cos(θ)\sin(θ)dθ
(dy)/(dx)=sqrt(5x+y)-5	\frac{dy}{dx}=\sqrt{5x+y}-5

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