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Popular Calculus Problems

derivative of (dy/(dx))-y=0	\frac{d}{dx}(\frac{dy}{dx})-y=0
integral of e^{4x}sin(7x)	\int\:e^{4x}\sin(7x)dx
integral of x^2cos(x/9)	\int\:x^{2}\cos(\frac{x}{9})dx
integral of (u^2)/(sqrt(u^2+25))	\int\:\frac{u^{2}}{\sqrt{u^{2}+25}}du
derivative of 3/5 x^{10}	derivative\:\frac{3}{5}x^{10}
integral of 1/((x+1/2)^2+3/4)	\int\:\frac{1}{(x+\frac{1}{2})^{2}+\frac{3}{4}}dx
integral of 6^3+3/x+1/(x^2)	\int\:6^{3}+\frac{3}{x}+\frac{1}{x^{2}}dx
inverse oflaplace {1/(S^2+3S)}	inverselaplace\:\left\{\frac{1}{S^{2}+3S}\right\}
integral of (3x^2+2x+1)	\int\:(3x^{2}+2x+1)dx
(\partial)/(\partial z)(2xz)	\frac{\partial\:}{\partial\:z}(2xz)
integral of (e^{1/x})/(x^2)	\int\:\frac{e^{\frac{1}{x}}}{x^{2}}dx
(\partial)/(\partial x)(sqrt(3x^2+2y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{3x^{2}+2y^{2}})
area y=x^2-3x,y=4x	area\:y=x^{2}-3x,y=4x
(x^2+1)(dy)/(dx)+7x(y-1)=0,y(0)=9	(x^{2}+1)\frac{dy}{dx}+7x(y-1)=0,y(0)=9
integral of x^2e^{21x}	\int\:x^{2}e^{21x}dx
2y^'+ty=2	2y^{\prime\:}+ty=2
integral from 4 to 9 of 1/(sqrt(x))	\int\:_{4}^{9}\frac{1}{\sqrt{x}}dx
limit as x approaches 5 of (x-5)/(\|x-5\|)	\lim\:_{x\to\:5}(\frac{x-5}{\left\|x-5\right\|})
limit as x approaches 15 of 2	\lim\:_{x\to\:15}(2)
derivative of (x^3+7/x)	\frac{d}{dx}(\frac{x^{3}+7}{x})
integral of sin^3(5x)cos^3(5x)	\int\:\sin^{3}(5x)\cos^{3}(5x)dx
derivative of (8+x^{1/x})	\frac{d}{dx}((8+x)^{\frac{1}{x}})
derivative of (x+2/(x^2))	\frac{d}{dx}(\frac{x+2}{x^{2}})
taylor tan(x), pi/4	taylor\:\tan(x),\frac{π}{4}
y^'=(2-e^x)/(3+2y),y(0)=0	y^{\prime\:}=\frac{2-e^{x}}{3+2y},y(0)=0
derivative of y= 1/(x+ke^x)	derivative\:y=\frac{1}{x+ke^{x}}
inverse oflaplace 8	inverselaplace\:8
derivative of tan^2(x)	derivative\:\tan^{2}(x)
derivative of x^2-ln(2)	\frac{d}{dx}(x^{2}-\ln(2))
limit as x approaches-1 of x/(3x+2)	\lim\:_{x\to\:-1}(\frac{x}{3x+2})
integral of ((e^x)/x)	\int\:(\frac{e^{x}}{x})dx
limit as h approaches-2 of (h^3+8)/(h+2)	\lim\:_{h\to\:-2}(\frac{h^{3}+8}{h+2})
derivative of 7x+4	\frac{d}{dx}(7x+4)
derivative of 2xsin(x+x^2cos(x))	\frac{d}{dx}(2x\sin(x)+x^{2}\cos(x))
area y=x^3-7x,y=9x	area\:y=x^{3}-7x,y=9x
laplacetransform t/5	laplacetransform\:\frac{t}{5}
integral from 2 to infinity of e^{-6p}	\int\:_{2}^{\infty\:}e^{-6p}dp
(\partial)/(\partial x)(-(v(x,t))/(b(x,t)x-b(x,t)v(x,t)t))	\frac{\partial\:}{\partial\:x}(-\frac{v(x,t)}{b(x,t)x-b(x,t)v(x,t)t})
integral of pisin(x)	\int\:π\sin(x)dx
limit as x approaches 6+of sqrt(x-6)	\lim\:_{x\to\:6+}(\sqrt{x-6})
derivative of (x^2/x)	\frac{d}{dx}(\frac{x^{2}}{x})
integral of \sqrt[7]{x^3}(1+sqrt(x))	\int\:\sqrt[7]{x^{3}}(1+\sqrt{x})dx
limit as x approaches 1.9 of-x^2+5x-2	\lim\:_{x\to\:1.9}(-x^{2}+5x-2)
limit as x approaches-5 of (-6x)/(x+5)	\lim\:_{x\to\:-5}(\frac{-6x}{x+5})
(dy)/(dt)=-3(y-2)	\frac{dy}{dt}=-3(y-2)
(\partial)/(\partial x)(sqrt(3x+2xy^2))	\frac{\partial\:}{\partial\:x}(\sqrt{3x+2xy^{2}})
derivative of y=arccos((11)/x)	derivative\:y=\arccos(\frac{11}{x})
integral of xe^xy	\int\:xe^{x}ydx
integral from 1 to ln(x) of 1/t	\int\:_{1}^{\ln(x)}\frac{1}{t}dt
integral of 1/(x^{2/3)}	\int\:\frac{1}{x^{\frac{2}{3}}}dx
tangent of y=(x^2)/(x+3),(2, 4/5)	tangent\:y=\frac{x^{2}}{x+3},(2,\frac{4}{5})
derivative of f(x)=4x^2+1	derivative\:f(x)=4x^{2}+1
y^'+1/2 y=8,y(0)=2	y^{\prime\:}+\frac{1}{2}y=8,y(0)=2
(\partial)/(\partial x)(((xv^2))/((x^2+v^2)))	\frac{\partial\:}{\partial\:x}(\frac{(xv^{2})}{(x^{2}+v^{2})})
integral of 5/((5x+4)ln(5x+4))	\int\:\frac{5}{(5x+4)\ln(5x+4)}dx
integral of 6x^2-2x+1	\int\:6x^{2}-2x+1dx
sum from n=1 to infinity of n/(n^3+3)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{3}+3}
derivative of y=\sqrt[3]{2x}	derivative\:y=\sqrt[3]{2x}
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)
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)((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))
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)})
(dy)/(dx)=(x^2-y^2)/(3xy)	\frac{dy}{dx}=\frac{x^{2}-y^{2}}{3xy}
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
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
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
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

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