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Popular Calculus Problems

x((dy)/(dx))+2y=0	x(\frac{dy}{dx})+2y=0
integral of (x^2-x)cos(x)	\int\:(x^{2}-x)\cos(x)dx
limit as x approaches 5-of 2/((x-5))	\lim\:_{x\to\:5-}(\frac{2}{(x-5)})
derivative of 3x^2e^x+e^x(x^3+5)	derivative\:3x^{2}e^{x}+e^{x}(x^{3}+5)
ye^{2x}dx-(4+e^{2x})dy=0	ye^{2x}dx-(4+e^{2x})dy=0
integral from 0 to 2pi of cos^4(x)	\int\:_{0}^{2π}\cos^{4}(x)dx
integral from 0 to pi/(20) of cos(10x)	\int\:_{0}^{\frac{π}{20}}\cos(10x)dx
sum from n=1 to infinity of (2^n)/n	\sum\:_{n=1}^{\infty\:}\frac{2^{n}}{n}
derivative of (x^2+x+1/(x^2+1))	\frac{d}{dx}(\frac{x^{2}+x+1}{x^{2}+1})
derivative of 1/2 (tan(x-x))	\frac{d}{dx}(\frac{1}{2}(\tan(x)-x))
sum from n=0 to infinity of n^3x^n	\sum\:_{n=0}^{\infty\:}n^{3}x^{n}
derivative of 9xarcsin(x)	\frac{d}{dx}(9x\arcsin(x))
derivative of sqrt(6x-5)	\frac{d}{dx}(\sqrt{6x-5})
integral of (x^3-2x+3)/(x-1)	\int\:\frac{x^{3}-2x+3}{x-1}dx
inverse oflaplace 1/((s+4)^2)	inverselaplace\:\frac{1}{(s+4)^{2}}
y^{''}-2y^'+y=t+1,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}+y=t+1,y(0)=0,y^{\prime\:}(0)=0
derivative of 5^{x+1}	\frac{d}{dx}(5^{x+1})
tangent of-3x^2	tangent\:-3x^{2}
derivative of 4/(4x+1)	\frac{d}{dx}(\frac{4}{4x+1})
integral of (4+8x)/(1+x^2)	\int\:\frac{4+8x}{1+x^{2}}dx
integral of 9x^2+4x-3	\int\:9x^{2}+4x-3dx
derivative of (2x-x^2/(sqrt(x))-3cot(x))	\frac{d}{dx}(\frac{2x-x^{2}}{\sqrt{x}}-3\cot(x))
limit as x approaches 4 of 2x^2+7	\lim\:_{x\to\:4}(2x^{2}+7)
(dh}{dt}=\frac{(7-e^{-t/5}))/6-2/9 h	\frac{dh}{dt}=\frac{(7-e^{-\frac{t}{5}})}{6}-\frac{2}{9}h
slope of 2xy^3=xy+6	slope\:2xy^{3}=xy+6
integral of sqrt(1/(4x)+9)	\int\:\sqrt{\frac{1}{4x}+9}dx
y^'=((x^4+x^2y^2+y^4))/(x^3y)	y^{\prime\:}=\frac{(x^{4}+x^{2}y^{2}+y^{4})}{x^{3}y}
laplacetransform t-2	laplacetransform\:t-2
derivative of y=log_{6}(x)	derivative\:y=\log_{6}(x)
limit as x approaches 2 of x^2	\lim\:_{x\to\:2}(x^{2})
integral of (sqrt(1+\sqrt{y)})/(sqrt(y))	\int\:\frac{\sqrt{1+\sqrt{y}}}{\sqrt{y}}dy
integral of (x-1)/((x^2+4x+5)(x+1))	\int\:\frac{x-1}{(x^{2}+4x+5)(x+1)}dx
(dy)/(dx)+x^2y=10x^2	\frac{dy}{dx}+x^{2}y=10x^{2}
y^{''}-3y^'+2y=4cos(4t)	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=4\cos(4t)
integral from 0 to 0.6 of 250x	\int\:_{0}^{0.6}250xdx
integral of-2sin(2t)	\int\:-2\sin(2t)dt
derivative of ln(x^{61})	derivative\:\ln(x^{61})
derivative of (5x/(sqrt(x^2+5)))	\frac{d}{dx}(\frac{5x}{\sqrt{x^{2}+5}})
integral from 0 to pi/2 of sin^2(2x)	\int\:_{0}^{\frac{π}{2}}\sin^{2}(2x)dx
integral of (3x-6)	\int\:(3x-6)dx
limit as x approaches 5-of 2/((x-5)^3)	\lim\:_{x\to\:5-}(\frac{2}{(x-5)^{3}})
derivative of (sin(x)/(3x^2))	\frac{d}{dx}(\frac{\sin(x)}{3x^{2}})
limit as x approaches 3 of g(x)	\lim\:_{x\to\:3}(g(x))
derivative of g(x)=(x-4)^3+3x(x-4)^2	derivative\:g(x)=(x-4)^{3}+3x(x-4)^{2}
(\partial)/(\partial x)(xye^{-9y})	\frac{\partial\:}{\partial\:x}(xye^{-9y})
inverse oflaplace a/s	inverselaplace\:\frac{a}{s}
integral from 2 to 6 of 7sqrt(x^3)	\int\:_{2}^{6}7\sqrt{x^{3}}dx
(\partial)/(\partial y)(5xy-10y)	\frac{\partial\:}{\partial\:y}(5xy-10y)
integral of 1/(t+1)	\int\:\frac{1}{t+1}dt
limit as x approaches infinity of \sqrt[3]{x/(x^2+3)}	\lim\:_{x\to\:\infty\:}(\sqrt[3]{\frac{x}{x^{2}+3}})
derivative of cos(bx)	\frac{d}{dx}(\cos(bx))
integral of kx^2	\int\:kx^{2}dx
taylor x*ln(x),1	taylor\:x\cdot\:\ln(x),1
integral of (-3cos(x)+4sec^2(x))	\int\:(-3\cdot\:\cos(x)+4\cdot\:\sec^{2}(x))dx
integral of 1/(sqrt(a-bx))	\int\:\frac{1}{\sqrt{a-bx}}dx
derivative of y=x^2-1	derivative\:y=x^{2}-1
xy^'+y+yln(xy)=0	xy^{\prime\:}+y+y\ln(xy)=0
limit as r approaches 0 of 1/(r^2)	\lim\:_{r\to\:0}(\frac{1}{r^{2}})
integral of 6e^{-0.4x}	\int\:6e^{-0.4x}dx
integral of 6/2	\int\:\frac{6}{2}dx
derivative of x^2*sin^2(x)	\frac{d}{dx}(x^{2}\cdot\:\sin^{2}(x))
tangent of f(x)=(36x)/(x^2+36),(-3,-12/5)	tangent\:f(x)=\frac{36x}{x^{2}+36},(-3,-\frac{12}{5})
derivative of (sin(x+cos(x))sec(x)dx)	\frac{d}{dx}((\sin(x)+\cos(x))\sec(x)dx)
derivative of (6x/(sqrt(x^2+2)))	\frac{d}{dx}(\frac{6x}{\sqrt{x^{2}+2}})
integral of t^2-cos(2pi)t	\int\:t^{2}-\cos(2π)tdt
integral of sin^2(t	\int\:\sin^{2}(d)t
derivative of (16x^3)	\frac{d}{dx}((16x)^{3})
derivative of f(x)=-2sin(2x)	derivative\:f(x)=-2\sin(2x)
integral of x^4-2x^2+1	\int\:x^{4}-2x^{2}+1dx
integral of (8x-9)	\int\:(8x-9)dx
integral of (2-3x^2)/(sqrt(5x^3-10x+5))	\int\:\frac{2-3x^{2}}{\sqrt{5x^{3}-10x+5}}dx
(\partial)/(\partial x)(x^2ye^{y/z})	\frac{\partial\:}{\partial\:x}(x^{2}ye^{\frac{y}{z}})
(\partial)/(\partial x)(sqrt(x)+y)	\frac{\partial\:}{\partial\:x}(\sqrt{x}+y)
limit as x approaches infinity of 4x^3(e^{-2/(x^3)}-1)	\lim\:_{x\to\:\infty\:}(4x^{3}(e^{-\frac{2}{x^{3}}}-1))
integral of sin^4(x	\int\:\sin^{4}(d)xdx
area x=y^2+6,y= x/2-3/2	area\:x=y^{2}+6,y=\frac{x}{2}-\frac{3}{2}
limit as t approaches 0 of cos(t)sin(t)	\lim\:_{t\to\:0}(\cos(t)\sin(t))
integral of cos^5(x)sin^2(x)	\int\:\cos^{5}(x)\sin^{2}(x)dx
tangent of 2y^3+xy-y=250x^4,(1,5)	tangent\:2y^{3}+xy-y=250x^{4},(1,5)
derivative of (1-cos(x)^2)	\frac{d}{dx}((1-\cos(x))^{2})
integral of 5xln(x^6)	\int\:5x\ln(x^{6})dx
limit as x approaches 1 of 3x^3-2x^2+4	\lim\:_{x\to\:1}(3x^{3}-2x^{2}+4)
integral of (x^2+2x)/(x^3-x^2+x-1)	\int\:\frac{x^{2}+2x}{x^{3}-x^{2}+x-1}dx
derivative of y(θ)= pi/9 cos(θ)	derivative\:y(θ)=\frac{π}{9}\cos(θ)
limit as x approaches 0 of 1/(x^2+x)	\lim\:_{x\to\:0}(\frac{1}{x^{2}+x})
integral of-8/(y^9)	\int\:-\frac{8}{y^{9}}dy
integral of (3x+2)/(x^3-x^2-2x)	\int\:\frac{3x+2}{x^{3}-x^{2}-2x}dx
area y=x^2-1,y=-x+2,x=0,x=1	area\:y=x^{2}-1,y=-x+2,x=0,x=1
derivative of 9xsin(x^2)	\frac{d}{dx}(9x\sin(x^{2}))
y^{''}+9y^'=0	y^{\prime\:\prime\:}+9y^{\prime\:}=0
y^'=3x^2y-8e^{(x^3-4x)}	y^{\prime\:}=3x^{2}y-8e^{(x^{3}-4x)}
y^{''}+4pi^2y=cos^3(2pix),y(0)=1	y^{\prime\:\prime\:}+4π^{2}y=\cos^{3}(2πx),y(0)=1
tangent of f(x)=5-5x^2,(5,-120)	tangent\:f(x)=5-5x^{2},(5,-120)
limit as x approaches 5 of x^2+2x-4	\lim\:_{x\to\:5}(x^{2}+2x-4)
integral of e^{13x}	\int\:e^{13x}dx
inverse oflaplace 1/(2s+6)	inverselaplace\:\frac{1}{2s+6}
(dy)/(dx)=piy+12	\frac{dy}{dx}=πy+12
integral of 8x(ln(x^5))^2	\int\:8x(\ln(x^{5}))^{2}dx
implicit (dy)/(dx),xy=0	implicit\:\frac{dy}{dx},xy=0
integral from 0 to pi of cos^2(x)	\int\:_{0}^{π}\cos^{2}(x)dx

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