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Popular Calculus Problems

2(d^2y)/(dx^2)+8y=cos(2x)	2\frac{d^{2}y}{dx^{2}}+8y=\cos(2x)
(\partial)/(\partial x)(2(x-1))	\frac{\partial\:}{\partial\:x}(2(x-1))
integral of 1/((x+3)^3)	\int\:\frac{1}{(x+3)^{3}}dx
integral from-1 to 2 of (y+2)-(y^2)	\int\:_{-1}^{2}(y+2)-(y^{2})dy
integral of tan(x)x	\int\:\tan(x)xdx
integral of (x^2+7x-6)/((x+1)(x^2-4x+7))	\int\:\frac{x^{2}+7x-6}{(x+1)(x^{2}-4x+7)}dx
integral of 8/(θ^2)cos(8/θ)	\int\:\frac{8}{θ^{2}}\cos(\frac{8}{θ})dθ
derivative of y=ln(8-4x)	derivative\:y=\ln(8-4x)
derivative of f(x)=sqrt(21x)	derivative\:f(x)=\sqrt{21x}
tangent of y=8xsin(x),(pi/2 ,4pi)	tangent\:y=8x\sin(x),(\frac{π}{2},4π)
tangent of y= 1/(x^5),(1,1)	tangent\:y=\frac{1}{x^{5}},(1,1)
(\partial)/(\partial x)((x_{1}+y_{2})^2)	\frac{\partial\:}{\partial\:x}((x_{1}+y_{2})^{2})
derivative of 3x+2	derivative\:3x+2
inverse oflaplace 2/((s+2)(s+1))	inverselaplace\:\frac{2}{(s+2)(s+1)}
integral of e^{8x+e^{8x}}	\int\:e^{8x+e^{8x}}dx
derivative of x^x(ln(x+1))	\frac{d}{dx}(x^{x}(\ln(x)+1))
(\partial)/(\partial y)(sqrt((x+2)/(y+2)))	\frac{\partial\:}{\partial\:y}(\sqrt{\frac{x+2}{y+2}})
derivative of x^3(x-8^2)	\frac{d}{dx}(x^{3}(x-8)^{2})
derivative of 1/(x-y)	\frac{d}{dx}(\frac{1}{x-y})
(dy)/(dx)+1/x y=0	\frac{dy}{dx}+\frac{1}{x}y=0
integral of 2cos(x/3)	\int\:2\cos(\frac{x}{3})dx
derivative of f(x)=x^2-6x-7	derivative\:f(x)=x^{2}-6x-7
xy^2y^'=y^3-5x^3	xy^{2}y^{\prime\:}=y^{3}-5x^{3}
d/(dθ)(tan^2(θ))	\frac{d}{dθ}(\tan^{2}(θ))
y^{''}+11y^'+24y=0,y(0)=0,y^'(0)=-7	y^{\prime\:\prime\:}+11y^{\prime\:}+24y=0,y(0)=0,y^{\prime\:}(0)=-7
limit as x approaches 0 of ((9^x-3^x))/x	\lim\:_{x\to\:0}(\frac{(9^{x}-3^{x})}{x})
integral of x*ln^3(x)	\int\:x\cdot\:\ln^{3}(x)dx
limit as x approaches 2 of 2x^2-3x+5	\lim\:_{x\to\:2}(2x^{2}-3x+5)
inverse oflaplace (s^2)/((s^2+1/4))	inverselaplace\:\frac{s^{2}}{(s^{2}+\frac{1}{4})}
integral of ((x+1)^2)/x	\int\:\frac{(x+1)^{2}}{x}dx
tangent of sin(3x)	tangent\:\sin(3x)
derivative of y=sqrt(e^x+1)	derivative\:y=\sqrt{e^{x}+1}
derivative of-2sin(2x+2cos(2x))	\frac{d}{dx}(-2\sin(2x)+2\cos(2x))
derivative of x/(x-8)	derivative\:\frac{x}{x-8}
limit as x approaches 0+of 2xe^{-3x}	\lim\:_{x\to\:0+}(2xe^{-3x})
integral from 0 to 16 of (500x)/(x^2+24)	\int\:_{0}^{16}\frac{500x}{x^{2}+24}dx
derivative of 5pix^2	derivative\:5πx^{2}
(\partial)/(\partial x)(40x^{3/4}y^{1/4})	\frac{\partial\:}{\partial\:x}(40x^{\frac{3}{4}}y^{\frac{1}{4}})
area y=x^3,x=-1	area\:y=x^{3},x=-1
tangent of f(x)=(x^3+1)(x^2-2),\at x=2	tangent\:f(x)=(x^{3}+1)(x^{2}-2),\at\:x=2
tangent of f(x)=(x-4)(3-x)^3,\at x=5	tangent\:f(x)=(x-4)(3-x)^{3},\at\:x=5
integral of x^2(3x+x^{-3})	\int\:x^{2}(3x+x^{-3})dx
integral of sin(-3x)	\int\:\sin(-3x)dx
limit as t approaches pi of-9sin(-t/2)	\lim\:_{t\to\:π}(-9\sin(-\frac{t}{2}))
integral of-3sqrt(x)+4x	\int\:-3\sqrt{x}+4xdx
derivative of x^{-3/4}	derivative\:x^{-\frac{3}{4}}
integral from 0 to pi/6 of (9sec^2(x))	\int\:_{0}^{\frac{π}{6}}(9\sec^{2}(x))dx
integral of 1/(7-3x)	\int\:\frac{1}{7-3x}dx
y^'=9x+y	y^{\prime\:}=9x+y
(2e^y-x)((dy)/(dx))=1	(2e^{y}-x)(\frac{dy}{dx})=1
derivative of f(x)=-7e^{-3x}-6e^{-3x}x	derivative\:f(x)=-7e^{-3x}-6e^{-3x}x
limit as x approaches 3 of (x^2-8)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{2}-8}{x-3})
derivative of sqrt(x)-3x^2+8x^{-2}	\frac{d}{dx}(\sqrt{x}-3x^{2}+8x^{-2})
(dy)/(dx)=y+4y*cos(2x)	\frac{dy}{dx}=y+4y\cdot\:\cos(2x)
integral of-1728-x^3	\int\:-1728-x^{3}dx
integral from 4 to 8 of 5/(12-x)	\int\:_{4}^{8}\frac{5}{12-x}dx
derivative of (arctan(5x)^2)	\frac{d}{dx}((\arctan(5x))^{2})
integral of (x^4+8x^2+8)/(x^3-4x)	\int\:\frac{x^{4}+8x^{2}+8}{x^{3}-4x}dx
taylor x^3-3x^2+5x-7,0	taylor\:x^{3}-3x^{2}+5x-7,0
slope of (1.7)(3.3)	slope\:(1.7)(3.3)
integral from 0 to 2 of ()/(sqrt(4+t^2))	\int\:_{0}^{2}\frac{dt}{\sqrt{4+t^{2}}}dx
y^{''}+49y=0,y(0)=4,y^'(0)=-6	y^{\prime\:\prime\:}+49y=0,y(0)=4,y^{\prime\:}(0)=-6
y^'-y=3x-3	y^{\prime\:}-y=3x-3
derivative of f(x)=1-1/(x+2)	derivative\:f(x)=1-\frac{1}{x+2}
tangent of-3/2 x^2+3x+3	tangent\:-\frac{3}{2}x^{2}+3x+3
integral of 1/r	\int\:\frac{1}{r}dr
derivative of (x^2/(9+2x))	\frac{d}{dx}(\frac{x^{2}}{9+2x})
tangent of x^2+2xy-y^2+x=12,(3,6)	tangent\:x^{2}+2xy-y^{2}+x=12,(3,6)
inverse oflaplace 3/s+8 1/(s(s+1))	inverselaplace\:\frac{3}{s}+8\frac{1}{s(s+1)}
integral of sin(x)-2cos(x)	\int\:\sin(x)-2\cos(x)dx
integral of (72)/(x^2sqrt(4x^2+9))	\int\:\frac{72}{x^{2}\sqrt{4x^{2}+9}}dx
sum from n=0 to infinity of (5x)^n	\sum\:_{n=0}^{\infty\:}(5x)^{n}
maclaurin 1/(1-x^2)	maclaurin\:\frac{1}{1-x^{2}}
tangent of y=sqrt(x),(4,2)	tangent\:y=\sqrt{x},(4,2)
derivative of 3x^2+12x+9	\frac{d}{dx}(3x^{2}+12x+9)
integral of 1/(36e^{-5x)+e^{5x}}	\int\:\frac{1}{36e^{-5x}+e^{5x}}dx
slope ofintercept (4)(8.8)	slopeintercept\:(4)(8.8)
integral of 9(9x+2)	\int\:9(9x+2)dx
taylor sin(2x),0.0001	taylor\:\sin(2x),0.0001
limit as x approaches 3 of [ 8/(8+10)]	\lim\:_{x\to\:3}([\frac{8}{8+10}])
(\partial)/(\partial y)(tan(y/x))	\frac{\partial\:}{\partial\:y}(\tan(\frac{y}{x}))
f(x)=sin(7x)	f(x)=\sin(7x)
slope of 1/3t^3-9t+2	slope\:\frac{1}{3}\cdot\:t^{3}-9\cdot\:t+2
integral of xsqrt(1+1/(4x))	\int\:x\sqrt{1+\frac{1}{4x}}dx
tangent of sqrt(3x+25),\at x=-3	tangent\:\sqrt{3x+25},\at\:x=-3
integral of (2x-1)ln(5x)	\int\:(2x-1)\ln(5x)dx
(dP)/(dt)=Psqrt(t)	\frac{dP}{dt}=P\sqrt{t}
integral of x^4ln(2x)	\int\:x^{4}\ln(2x)dx
derivative of x^{2ax}	\frac{d}{dx}(x^{2ax})
derivative of f(b)= b/(z+n)	derivative\:f(b)=\frac{b}{z+n}
integral of ((6x^2+5x+6))/((x^2+1)^2)	\int\:\frac{(6x^{2}+5x+6)}{(x^{2}+1)^{2}}dx
(dS)/(dr)=kS	\frac{dS}{dr}=kS
integral of sin^3(u)	\int\:\sin^{3}(u)du
derivative of (ln(x)^{-1})	\frac{d}{dx}((\ln(x))^{-1})
derivative of y=x^{4/3}	derivative\:y=x^{\frac{4}{3}}
inverse oflaplace 1/(s^2-1)	inverselaplace\:\frac{1}{s^{2}-1}
integral from 0 to pi of cos(x)sin(x)	\int\:_{0}^{π}\cos(x)\sin(x)dx
integral from 0 to pi/6 of 64sin^2(x)	\int\:_{0}^{\frac{π}{6}}64\sin^{2}(x)dx
integral of (cos(pi/(x^{31)}))/(x^{32)}	\int\:\frac{\cos(\frac{π}{x^{31}})}{x^{32}}dx
derivative of y=(e^x)/(1+e^x)	derivative\:y=\frac{e^{x}}{1+e^{x}}

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