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Popular Calculus Problems

y^'(y^3-x)=y	y^{\prime\:}(y^{3}-x)=y
integral of 1/(x+9)	\int\:\frac{1}{x+9}dx
derivative of xarcsin(x+sqrt(1-x^2))	\frac{d}{dx}(x\arcsin(x)+\sqrt{1-x^{2}})
y^{''}+8y^'+41y=0,y(0)=2,y^'(0)=-7	y^{\prime\:\prime\:}+8y^{\prime\:}+41y=0,y(0)=2,y^{\prime\:}(0)=-7
integral from-1 to 1 of 1/(x^{2/3)}	\int\:_{-1}^{1}\frac{1}{x^{\frac{2}{3}}}dx
derivative of ((x+1/x)^3)	\frac{d}{dx}((\frac{x+1}{x})^{3})
derivative of (x^2/(x^2-16))	\frac{d}{dx}(\frac{x^{2}}{x^{2}-16})
integral of x^9ln(x)	\int\:x^{9}\ln(x)dx
tangent of f(x)=(13x-1)^{-1/3},\at x=5	tangent\:f(x)=(13x-1)^{-\frac{1}{3}},\at\:x=5
derivative of t/((t-9)^2)	derivative\:\frac{t}{(t-9)^{2}}
25y^{''}+30y^'+9y=0	25y^{\prime\:\prime\:}+30y^{\prime\:}+9y=0
(\partial)/(\partial x)(2x^{0.3}y^{0.3}+1)	\frac{\partial\:}{\partial\:x}(2x^{0.3}y^{0.3}+1)
integral of (3x^{8/3})/8+C	\int\:\frac{3x^{\frac{8}{3}}}{8}+Cdx
integral of arccot(5x)	\int\:\arccot(5x)dx
y^'+2/3 y=1-1/2 t	y^{\prime\:}+\frac{2}{3}y=1-\frac{1}{2}t
derivative of A(4e^{2x}x+4e^{2x})	\frac{d}{dx}(A(4e^{2x}x+4e^{2x}))
derivative of (x^5+2x(x^3+x^2+x+7))	\frac{d}{dx}((x^{5}+2x)(x^{3}+x^{2}+x+7))
integral of 1/((x+3)^2)	\int\:\frac{1}{(x+3)^{2}}dx
area y=9x^2ln(x),y=36ln(x)	area\:y=9x^{2}\ln(x),y=36\ln(x)
laplacetransform cos^2(t)	laplacetransform\:\cos^{2}(t)
limit as x approaches-1 of x^3+x^2-6x+9	\lim\:_{x\to\:-1}(x^{3}+x^{2}-6x+9)
integral of x/((x+2)(5x-1))	\int\:\frac{x}{(x+2)(5x-1)}dx
(d^2)/(dx^2)(tan(5x+2))	\frac{d^{2}}{dx^{2}}(\tan(5x+2))
integral of (16x)/((sqrt(x^2-9))^5)	\int\:\frac{16x}{(\sqrt{x^{2}-9})^{5}}dx
y^'=2y(1-0.2y)	y^{\prime\:}=2y(1-0.2y)
integral of 4 1/((4-x^2)^{3/2)}	\int\:4\frac{1}{(4-x^{2})^{\frac{3}{2}}}dx
integral of (7sin(x))/(cos^3(x))	\int\:\frac{7\sin(x)}{\cos^{3}(x)}dx
integral of 1/(xln(x^9))	\int\:\frac{1}{x\ln(x^{9})}dx
integral from 0 to 1 of sqrt(2/(2-x^2))	\int\:_{0}^{1}\sqrt{\frac{2}{2-x^{2}}}dx
derivative of y=3x-1	derivative\:y=3x-1
derivative of f(x)=e^x(x+xsqrt(x))	derivative\:f(x)=e^{x}(x+x\sqrt{x})
(dy)/(dx)=y-y^2	\frac{dy}{dx}=y-y^{2}
tangent of f(x)=-x^3,(1,-1)	tangent\:f(x)=-x^{3},(1,-1)
derivative of x^2-5x+5	derivative\:x^{2}-5x+5
integral of-7tan^3(x)	\int\:-7\tan^{3}(x)dx
integral of 2te^t	\int\:2te^{t}dt
integral of (A+BT+CT^2+DT^2) 1/T	\int\:(A+BT+CT^{2}+DT^{2})\frac{1}{T}dT
integral of e^{3x}(3x^2y+2xy+y^3)	\int\:e^{3x}(3x^{2}y+2xy+y^{3})dx
integral of (x^5+4)/(x^3+x^2)	\int\:\frac{x^{5}+4}{x^{3}+x^{2}}dx
integral from 0 to R of sqrt(R^2-x^2)	\int\:_{0}^{R}\sqrt{R^{2}-x^{2}}dx
y^'-3y=0	y^{\prime\:}-3y=0
integral of 5cos(x)+4sin(x)	\int\:5\cos(x)+4\sin(x)dx
(\partial)/(\partial y)((x^3+(y/2))^{2/3})	\frac{\partial\:}{\partial\:y}((x^{3}+(\frac{y}{2}))^{\frac{2}{3}})
derivative of 765480	\frac{d}{dx}(765480)
y^{''}+y^'-3y=0	y^{\prime\:\prime\:}+y^{\prime\:}-3y=0
integral of 10xex^2	\int\:10xex^{2}dx
derivative of 800-800x^{-1}	\frac{d}{dx}(800-800x^{-1})
(\partial}{\partial t}(\frac{sin(t))/t)	\frac{\partial\:}{\partial\:t}(\frac{\sin(t)}{t})
sum from n=1 to infinity of (0.1)^{n-1}	\sum\:_{n=1}^{\infty\:}(0.1)^{n-1}
(\partial)/(\partial x)(tan(4x))	\frac{\partial\:}{\partial\:x}(\tan(4x))
d/(dt)(t^2-t)	\frac{d}{dt}(t^{2}-t)
(d^2)/(dx^2)(2^x)	\frac{d^{2}}{dx^{2}}(2^{x})
xy^'+3y=5x^2	xy^{\prime\:}+3y=5x^{2}
(\partial)/(\partial t)(e^{-t}cos(pix))	\frac{\partial\:}{\partial\:t}(e^{-t}\cos(πx))
derivative of y=((6-5x)/(x^2-1))^2	derivative\:y=(\frac{6-5x}{x^{2}-1})^{2}
integral of 1/(sqrt(x)(\sqrt{x)-7)}	\int\:\frac{1}{\sqrt{x}(\sqrt{x}-7)}dx
d/(dy)((x^2y^2+2xy^3)/((x+y)^2))	\frac{d}{dy}(\frac{x^{2}y^{2}+2xy^{3}}{(x+y)^{2}})
integral of xsin(sqrt(x))	\int\:x\sin(\sqrt{x})dx
derivative of (2-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{2-\sec(x)}{\tan(x)})
area y=2-3x,x=-2,x=2,y=0	area\:y=2-3x,x=-2,x=2,y=0
integral from-2 to 2 of x^3	\int\:_{-2}^{2}x^{3}dx
derivative of y=4sqrt(x)	derivative\:y=4\sqrt{x}
x^'=(x-9)^2	x^{\prime\:}=(x-9)^{2}
derivative of 6xy	derivative\:6xy
limit as x approaches 0-of (-x)^{-x}	\lim\:_{x\to\:0-}((-x)^{-x})
derivative of (3x^3-2x^2*(3x^4+x^2))	\frac{d}{dx}((3x^{3}-2x^{2})\cdot\:(3x^{4}+x^{2}))
integral of (20)/((x-1)*(x^2+9))	\int\:\frac{20}{(x-1)\cdot\:(x^{2}+9)}dx
y^3-2x-2dx+3y^2xdy=0	y^{3}-2x-2dx+3y^{2}xdy=0
derivative of sec(xtan(x)(sqrt(x))(x+1))	\frac{d}{dx}(\sec(x)\tan(x)(\sqrt{x})(x+1))
(\partial)/(\partial x)(8xe^{xy})	\frac{\partial\:}{\partial\:x}(8xe^{xy})
sum from n=1 to infinity of (n!)/(n2^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n2^{n}}
integral of 7x^2sin(pix)	\int\:7x^{2}\sin(πx)dx
(dy)/(dx)= 1/(y-x)	\frac{dy}{dx}=\frac{1}{y-x}
integral of x^2-4x+7	\int\:x^{2}-4x+7dx
limit as x approaches-1 of (x^2-3)/(1-x)	\lim\:_{x\to\:-1}(\frac{x^{2}-3}{1-x})
(\partial)/(\partial x)(sin(x^2y-4xy^2))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}y-4xy^{2}))
integral of 7/((t^2+1)^{3/2)}	\int\:\frac{7}{(t^{2}+1)^{\frac{3}{2}}}dt
derivative of 4/(3x^2)	derivative\:\frac{4}{3x^{2}}
tangent of f(x)=x^2-1/x ,(-1,0)	tangent\:f(x)=x^{2}-\frac{1}{x},(-1,0)
integral from 0 to 2 of (x+2)/(x-4)	\int\:_{0}^{2}\frac{x+2}{x-4}dx
derivative of x^{2/3}	derivative\:x^{\frac{2}{3}}
derivative of (x^3+2x^{37})	\frac{d}{dx}((x^{3}+2x)^{37})
(\partial)/(\partial y)(x^3y^4+x^4y^3)	\frac{\partial\:}{\partial\:y}(x^{3}y^{4}+x^{4}y^{3})
derivative of-(10x/((x^2-9)^2))	\frac{d}{dx}(-\frac{10x}{(x^{2}-9)^{2}})
derivative of \sqrt[3]{x^3-9x}	\frac{d}{dx}(\sqrt[3]{x^{3}-9x})
taylor sin(cos(x))	taylor\:\sin(\cos(x))
limit as x approaches 0-of e^{9/x}	\lim\:_{x\to\:0-}(e^{\frac{9}{x}})
limit as x approaches infinity of x*0	\lim\:_{x\to\:\infty\:}(x\cdot\:0)
implicit (dy)/(dx),xy+4=x	implicit\:\frac{dy}{dx},xy+4=x
x^2(dy)/(dx)=y-xy,y(-1)=-6	x^{2}\frac{dy}{dx}=y-xy,y(-1)=-6
integral from 0 to 1 of 1/(x^{0.3)}	\int\:_{0}^{1}\frac{1}{x^{0.3}}dx
derivative of (x+1/(2x+5))	\frac{d}{dx}(\frac{x+1}{2x+5})
limit as x approaches 0+of ((36-4x^2))/x	\lim\:_{x\to\:0+}(\frac{(36-4x^{2})}{x})
derivative of 10sec^2(x)	\frac{d}{dx}(10\sec^{2}(x))
integral from 0 to 1 of 2piy(y-y^7)	\int\:_{0}^{1}2πy(y-y^{7})dy
integral of-2x^5	\int\:-2x^{5}dx
(\partial)/(\partial y)(sqrt(x+2)-y)	\frac{\partial\:}{\partial\:y}(\sqrt{x+2}-y)
integral from 0 to 5 of 1/(x^{12/13)}	\int\:_{0}^{5}\frac{1}{x^{\frac{12}{13}}}dx
area x^2-4,0,-4,3	area\:x^{2}-4,0,-4,3
(\partial)/(\partial y)(cos(x-y))	\frac{\partial\:}{\partial\:y}(\cos(x-y))

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