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Popular Calculus Problems

(dx)/(dt)+x^2=x	\frac{dx}{dt}+x^{2}=x
(\partial)/(\partial y)(ln(x+2y))	\frac{\partial\:}{\partial\:y}(\ln(x+2y))
derivative of f(x)=ln^2(x)	derivative\:f(x)=\ln^{2}(x)
maclaurin 4/(1+x)	maclaurin\:\frac{4}{1+x}
derivative of sin(2x^4)	\frac{d}{dx}(\sin(2x^{4}))
derivative of 1/(-sin(x))	\frac{d}{dx}(\frac{1}{-\sin(x)})
derivative of \sqrt[4]{2x^2-4x+7}	\frac{d}{dx}(\sqrt[4]{2x^{2}-4x+7})
integral of ((1-((x^2)/9)))^{1/2}	\int\:((1-(\frac{x^{2}}{9})))^{\frac{1}{2}}dx
d/(dy)(x^2+y^3)	\frac{d}{dy}(x^{2}+y^{3})
integral of (x+2)(x-5)	\int\:(x+2)(x-5)dx
derivative of e^{(x^4/(10)})	\frac{d}{dx}(e^{\frac{x^{4}}{10}})
(dy)/(dx)=x^2+y-1	\frac{dy}{dx}=x^{2}+y-1
y^{''}+9y=2sin(2x),y(0)=0,y^'(0)=-1	y^{\prime\:\prime\:}+9y=2\sin(2x),y(0)=0,y^{\prime\:}(0)=-1
tangent of (4x)/((x^2+1))	tangent\:\frac{4x}{(x^{2}+1)}
integral from 0 to 3 of (1+6x^2-10x^4)	\int\:_{0}^{3}(1+6x^{2}-10x^{4})dx
maclaurin (1+px)^{-1}	maclaurin\:(1+px)^{-1}
derivative of 8/(ln(x))	derivative\:\frac{8}{\ln(x)}
maclaurin sec^2(x)	maclaurin\:\sec^{2}(x)
integral of (cos(8x))/(cos^2(4x))	\int\:\frac{\cos(8x)}{\cos^{2}(4x)}dx
integral of 1+sin^2(x)	\int\:1+\sin^{2}(x)dx
integral of 1/(9-sqrt(x))	\int\:\frac{1}{9-\sqrt{x}}dx
integral of sin((3x)/2)	\int\:\sin(\frac{3x}{2})dx
integral of sin^7(x)cos^3(x)	\int\:\sin^{7}(x)\cos^{3}(x)dx
limit as x approaches 0 of x^{19x}	\lim\:_{x\to\:0}(x^{19x})
integral from 1 to infinity of f(x)	\int\:_{1}^{\infty\:}f(x)dx
(19xy^2-15y)+(19x^2y-15x)y^'=0	(19xy^{2}-15y)+(19x^{2}y-15x)y^{\prime\:}=0
integral of (sec(x)+cos(x))/(7cos(x))	\int\:\frac{\sec(x)+\cos(x)}{7\cos(x)}dx
derivative of x^4 1/8+1/(4x^2)	\frac{d}{dx}(x^{4}\frac{1}{8}+\frac{1}{4x^{2}})
derivative of (6x+1^2)	\frac{d}{dx}((6x+1)^{2})
y^{''}-25y=0	y^{\prime\:\prime\:}-25y=0
y^'+27y= 1/(x^2)	y^{\prime\:}+27y=\frac{1}{x^{2}}
integral of x/((1-x^2)^{1/2)}	\int\:\frac{x}{(1-x^{2})^{\frac{1}{2}}}dx
x^4+y^3sqrt(x^5+4)y^'=0	x^{4}+y^{3}\sqrt{x^{5}+4}y^{\prime\:}=0
sum from n=1 to infinity of 2/(3^{n-1)}	\sum\:_{n=1}^{\infty\:}\frac{2}{3^{n-1}}
integral of 5cot^4(x)	\int\:5\cot^{4}(x)dx
integral from 1 to 2 of 1/(x^2)-4/(x^3)	\int\:_{1}^{2}\frac{1}{x^{2}}-\frac{4}{x^{3}}dx
d/(dt)({f}(t))	\frac{d}{dt}({f}(t))
derivative of (5x^2-3x^5/(-sqrt(x)))	\frac{d}{dx}(\frac{5x^{2}-3x^{5}}{-\sqrt{x}})
integral from-infinity to infinity of x	\int\:_{-\infty\:}^{\infty\:}xdx
integral of e^{-2x}(x^2-3x+4)	\int\:e^{-2x}(x^{2}-3x+4)dx
inverse oflaplace s/(s^2-2s+5)	inverselaplace\:\frac{s}{s^{2}-2s+5}
derivative of (8-2x^3)^3	derivative\:(8-2x^{3})^{3}
integral of 1/(xsqrt(9+x^2))	\int\:\frac{1}{x\sqrt{9+x^{2}}}dx
(\partial)/(\partial x)(xy-ln(x^2-y^2))	\frac{\partial\:}{\partial\:x}(xy-\ln(x^{2}-y^{2}))
5x^2y^'=y^'+6xe^{-y}	5x^{2}y^{\prime\:}=y^{\prime\:}+6xe^{-y}
(\partial)/(\partial x)((x^2+y^2+z^2)^{-1/4})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2}+z^{2})^{-\frac{1}{4}})
limit as x approaches 0 of (x-2)/x	\lim\:_{x\to\:0}(\frac{x-2}{x})
(\partial)/(\partial y)(-8y^3+4xy+4x^2+9y^2)	\frac{\partial\:}{\partial\:y}(-8y^{3}+4xy+4x^{2}+9y^{2})
(\partial)/(\partial x)(x/(10)cos(5x))	\frac{\partial\:}{\partial\:x}(\frac{x}{10}\cos(5x))
integral from-2 to 3 of-x^2+x+6	\int\:_{-2}^{3}-x^{2}+x+6dx
integral of (x+y)^{-2}(x^2+2xy-y^2)	\int\:(x+y)^{-2}(x^{2}+2xy-y^{2})dx
integral of-(e^{4x})/x	\int\:-\frac{e^{4x}}{x}dx
derivative of cos(x-1/2 x)	\frac{d}{dx}(\cos(x)-\frac{1}{2}x)
(\partial)/(\partial x)((x+3y)^2)	\frac{\partial\:}{\partial\:x}((x+3y)^{2})
v^2dx+x(x+v)dv=0	v^{2}dx+x(x+v)dv=0
integral of (x^3+2x+5)/(x^2)	\int\:\frac{x^{3}+2x+5}{x^{2}}dx
integral from-2 to 1 of 2-x-x^2	\int\:_{-2}^{1}2-x-x^{2}dx
sum from n=0 to infinity of n/((n-2)!)	\sum\:_{n=0}^{\infty\:}\frac{n}{(n-2)!}
derivative of (x^2-3x+8/(x^2+9))	\frac{d}{dx}(\frac{x^{2}-3x+8}{x^{2}+9})
integral of sqrt(12+4x^2)	\int\:\sqrt{12+4x^{2}}dx
derivative of ((1+sin(x)/(1-cos(x)))^2)	\frac{d}{dx}((\frac{1+\sin(x)}{1-\cos(x)})^{2})
integral from-3 to 2 of (-x^2-x+6)	\int\:_{-3}^{2}(-x^{2}-x+6)dx
integral of (3y^2+6y)(y^3+3y^2+1)^{2/3}	\int\:(3y^{2}+6y)(y^{3}+3y^{2}+1)^{\frac{2}{3}}dy
tangent of f(x)=x^2-8	tangent\:f(x)=x^{2}-8
derivative of (x+3/(\|x+3\|))	\frac{d}{dx}(\frac{x+3}{\left\|x+3\right\|})
limit as x approaches 0+of ((ln(x))^2)/x	\lim\:_{x\to\:0+}(\frac{(\ln(x))^{2}}{x})
(\partial)/(\partial x)(sin^4(x))	\frac{\partial\:}{\partial\:x}(\sin^{4}(x))
slope of (-4,6),(3,-8)	slope\:(-4,6),(3,-8)
integral of (4x^3-2)x^2	\int\:(4x^{3}-2)x^{2}dx
sum from n=1 to infinity of (n!)/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{5^{n}}
derivative of f(x)= 1/(x^{16)}	derivative\:f(x)=\frac{1}{x^{16}}
integral of (x^3)/3	\int\:\frac{x^{3}}{3}dx
inverse oflaplace te^t	inverselaplace\:te^{t}
(d^7)/(dx^7)((2x+5)^7)	\frac{d^{7}}{dx^{7}}((2x+5)^{7})
derivative of (6-sec(x))/(tan(x))	derivative\:\frac{6-\sec(x)}{\tan(x)}
integral of 1/(10sqrt(x))	\int\:\frac{1}{10\sqrt{x}}dx
(\partial)/(\partial x)((8y)/(9x^2+4y^2+5))	\frac{\partial\:}{\partial\:x}(\frac{8y}{9x^{2}+4y^{2}+5})
(dy)/(dx)=-sin^2(y)	\frac{dy}{dx}=-\sin^{2}(y)
sum from n=1 to infinity of (-1)^n(-1)^n	\sum\:_{n=1}^{\infty\:}(-1)^{n}(-1)^{n}
derivative of 5x^{ln(x})	\frac{d}{dx}(5x^{\ln(x)})
(dy)/(dx)y=x^x	\frac{dy}{dx}y=x^{x}
tangent of 8x^3-18x^2-6	tangent\:8x^{3}-18x^{2}-6
integral of-2x+18x^2-4x^3+16	\int\:-2x+18x^{2}-4x^{3}+16dx
limit as x approaches 3 of 4x^2-2x-6	\lim\:_{x\to\:3}(4x^{2}-2x-6)
normal of y=(sqrt(x))/(x+9),(1,0.1)	normal\:y=\frac{\sqrt{x}}{x+9},(1,0.1)
limit as x approaches infinity of-5x^2	\lim\:_{x\to\:\infty\:}(-5x^{2})
derivative of f(x)= 5/(x^2)+sin(x)	derivative\:f(x)=\frac{5}{x^{2}}+\sin(x)
x^'=0.1078*(1-x/(105900))x-x	x^{\prime\:}=0.1078\cdot\:(1-\frac{x}{105900})x-x
sum from n=1 to infinity of (15)/n	\sum\:_{n=1}^{\infty\:}\frac{15}{n}
integral from 0 to 1 of xe^{2x}	\int\:_{0}^{1}xe^{2x}dx
y^'+4y=6	y^{\prime\:}+4y=6
derivative of-6.25t^2+50t	derivative\:-6.25t^{2}+50t
(x^2+4xy)dx+xdy=0	(x^{2}+4xy)dx+xdy=0
limit as x approaches 1 of 5/((x-1)^2)	\lim\:_{x\to\:1}(\frac{5}{(x-1)^{2}})
derivative of (1+2x+3x^2+4x^3^{100})	\frac{d}{dx}((1+2x+3x^{2}+4x^{3})^{100})
inverse oflaplace (10)/((s-2)(s^3+s))	inverselaplace\:\frac{10}{(s-2)(s^{3}+s)}
2ty^'=4y	2ty^{\prime\:}=4y
(dP)/(dt)=0.08P(1-P/(1000))	\frac{dP}{dt}=0.08P(1-\frac{P}{1000})
integral of (x^2)/(sqrt((21+4x-x^2)))	\int\:\frac{x^{2}}{\sqrt{(21+4x-x^{2})}}dx
derivative of (d/(dx(e^x))/(1+x))	\frac{d}{dx}(\frac{\frac{d}{dx}(e^{x})}{1+x})

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