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Popular Calculus Problems

derivative of ln^3(2x+5)	\frac{d}{dx}(\ln^{3}(2x+5))
xy^'+y=x^4y^3	xy^{\prime\:}+y=x^{4}y^{3}
derivative of (6x-7^3(8x^2+9)^2)	\frac{d}{dx}((6x-7)^{3}(8x^{2}+9)^{2})
integral from 0 to 5 of (5-x)	\int\:_{0}^{5}(5-x)dx
xydy=ydx	xydy=ydx
area 4/x , 4/(x^2),x=7	area\:\frac{4}{x},\frac{4}{x^{2}},x=7
9y^{''}-y=xe^{x/3}	9y^{\prime\:\prime\:}-y=xe^{\frac{x}{3}}
implicit (dy)/(dx),x+y=xy	implicit\:\frac{dy}{dx},x+y=xy
derivative of 2x^2-1/x	\frac{d}{dx}(2x^{2}-\frac{1}{x})
integral from 0 to 8 of 1	\int\:_{0}^{8}1
limit as x approaches 3 of x^2-4x+10	\lim\:_{x\to\:3}(x^{2}-4x+10)
integral of tan^3(5x)sec(5x)	\int\:\tan^{3}(5x)\sec(5x)dx
integral of (x-1)/(x^2+x-6)	\int\:\frac{x-1}{x^{2}+x-6}dx
(x+y)^2dx+(2xy+x^2-3)dy=0,y(1)=1	(x+y)^{2}dx+(2xy+x^{2}-3)dy=0,y(1)=1
limit as x approaches 3/2 of (4x^2+12x+9)/(2x-3)	\lim\:_{x\to\:\frac{3}{2}}(\frac{4x^{2}+12x+9}{2x-3})
(dy)/(dx)=((y^2+y))/(x^2+x)	\frac{dy}{dx}=\frac{(y^{2}+y)}{x^{2}+x}
integral from 0 to infinity of xe^{-x/2}	\int\:_{0}^{\infty\:}xe^{-\frac{x}{2}}dx
integral from 0 to pi of 5e^xsin(x)	\int\:_{0}^{π}5e^{x}\sin(x)dx
sum from n=1 to infinity of 2	\sum\:_{n=1}^{\infty\:}2
derivative of ((x+6)/(x-6))^5	derivative\:(\frac{x+6}{x-6})^{5}
derivative of e^{-x/3}	\frac{d}{dx}(e^{-\frac{x}{3}})
integral of (1-x^2)^2x^2	\int\:(1-x^{2})^{2}x^{2}dx
area y=3x^4-3x^2,y=8x^2	area\:y=3x^{4}-3x^{2},y=8x^{2}
derivative of y=(2x-3)^4(x^2+x+1)^5	derivative\:y=(2x-3)^{4}(x^{2}+x+1)^{5}
derivative of a^{6x^2}	\frac{d}{dx}(a^{6x^{2}})
integral of (x^2)/(4x)	\int\:\frac{x^{2}}{4x}dx
x^2y^'+3xy=e^x	x^{2}y^{\prime\:}+3xy=e^{x}
2y^{''}-2y^'+13y=0	2y^{\prime\:\prime\:}-2y^{\prime\:}+13y=0
integral of 1/(5000x-x^2)	\int\:\frac{1}{5000x-x^{2}}dx
integral from 0 to 9 of \|sqrt(2x+8)-x\|	\int\:_{0}^{9}\left\|\sqrt{2x+8}-x\right\|dx
integral from 0 to pi/4 of 1-4sin^2(x)	\int\:_{0}^{\frac{π}{4}}1-4\sin^{2}(x)dx
integral of 2usin(u)	\int\:2u\sin(u)du
(dy}{dx}=\frac{x+y)/x	\frac{dy}{dx}=\frac{x+y}{x}
limit as x approaches 5 of x^5-9x+1	\lim\:_{x\to\:5}(x^{5}-9x+1)
integral of-4sin(x)	\int\:-4\sin(x)dx
limit as t approaches 2 of t^3i+t^4j+t^5k	\lim\:_{t\to\:2}(t^{3}i+t^{4}j+t^{5}k)
(\partial)/(\partial x)(x^4+3xy^2-3y^2)	\frac{\partial\:}{\partial\:x}(x^{4}+3xy^{2}-3y^{2})
integral from 0 to 4 of (1+3x-x^2)	\int\:_{0}^{4}(1+3x-x^{2})dx
derivative of-4x^5+6x^7	derivative\:-4x^{5}+6x^{7}
limit as x approaches+0 of (e^x-1)/(5x)	\lim\:_{x\to\:+0}(\frac{e^{x}-1}{5x})
tangent of f(x)=19x-1.86x^2,\at x=1	tangent\:f(x)=19x-1.86x^{2},\at\:x=1
(\partial}{\partial x}(\frac{10)/x)	\frac{\partial\:}{\partial\:x}(\frac{10}{x})
tangent of f(x)=(2x)/(x+1),\at x=1	tangent\:f(x)=\frac{2x}{x+1},\at\:x=1
(dy)/(dx)+4xy^2=0	\frac{dy}{dx}+4xy^{2}=0
integral of (4x^3)/(x^4+1)	\int\:\frac{4x^{3}}{x^{4}+1}dx
derivative of ((2t+1)^{3/2})/3	derivative\:\frac{(2t+1)^{\frac{3}{2}}}{3}
(dy)/(dx)=2^xln(2)+2/(x^2+1)	\frac{dy}{dx}=2^{x}\ln(2)+\frac{2}{x^{2}+1}
area x^2+4,-x^2-1,-2,3	area\:x^{2}+4,-x^{2}-1,-2,3
(\partial)/(\partial x)(cos(-t+y+e^x))	\frac{\partial\:}{\partial\:x}(\cos(-t+y+e^{x}))
derivative of ln(cos(ln(x)))	\frac{d}{dx}(\ln(\cos(\ln(x))))
(dy)/(dt)=3te^{-y}	\frac{dy}{dt}=3te^{-y}
derivative of y=xarcsin(2x)	derivative\:y=x\arcsin(2x)
(\partial)/(\partial x)(3x^3y-4/x+2y^{1/2})	\frac{\partial\:}{\partial\:x}(3x^{3}y-\frac{4}{x}+2y^{\frac{1}{2}})
integral from 1/7 to 3 of 8xln(7x)	\int\:_{\frac{1}{7}}^{3}8x\ln(7x)dx
tangent of y=3x+6cos(x),\at (pi/3)	tangent\:y=3x+6\cos(x),\at\:(\frac{π}{3})
inverse oflaplace s/(s^2+2s+3)	inverselaplace\:\frac{s}{s^{2}+2s+3}
derivative of f(x)=(2x^3-3x+1)/x	derivative\:f(x)=\frac{2x^{3}-3x+1}{x}
slope of y=x^2-2	slope\:y=x^{2}-2
laplacetransform e^{-t}(t^2)	laplacetransform\:e^{-t}(t^{2})
derivative of f(x)=sqrt(x)+\sqrt[7]{x}	derivative\:f(x)=\sqrt{x}+\sqrt[7]{x}
derivative of-x^3+3x	\frac{d}{dx}(-x^{3}+3x)
(\partial)/(\partial x)((x+y)^5+(x-y)^5)	\frac{\partial\:}{\partial\:x}((x+y)^{5}+(x-y)^{5})
tangent of f(x)=tan^2(x),\at x=-pi/4	tangent\:f(x)=\tan^{2}(x),\at\:x=-\frac{π}{4}
derivative of f(x)=13xe^x	derivative\:f(x)=13xe^{x}
derivative of y=\sqrt[3]{1+8x}	derivative\:y=\sqrt[3]{1+8x}
integral of 1/(sqrt(2pi))e^{-(x^2)/2}	\int\:\frac{1}{\sqrt{2π}}e^{-\frac{x^{2}}{2}}dx
integral of (5x+12)/(x(x^2+4))	\int\:\frac{5x+12}{x(x^{2}+4)}dx
integral of (x+1)^{-8}x	\int\:(x+1)^{-8}xdx
limit as x approaches 8 of sqrt(7x-4)	\lim\:_{x\to\:8}(\sqrt{7x-4})
sum from n=0 to infinity of 1.002^n	\sum\:_{n=0}^{\infty\:}1.002^{n}
integral from 0 to 2 of xe^{x^2}	\int\:_{0}^{2}xe^{x^{2}}dx
integral of (3x^2-7)/(x^3)	\int\:\frac{3x^{2}-7}{x^{3}}dx
area y=x+2,y=-1,x=2,x=5	area\:y=x+2,y=-1,x=2,x=5
derivative of sqrt(9z-8)	derivative\:\sqrt{9z-8}
integral of sqrt(x^4+4x^2)	\int\:\sqrt{x^{4}+4x^{2}}dx
integral of (x-7)/(x^2-x-12)	\int\:\frac{x-7}{x^{2}-x-12}dx
(\partial)/(\partial x)(8xe^{5xy})	\frac{\partial\:}{\partial\:x}(8xe^{5xy})
sum from n=0 to infinity of (n!)/(11^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{11^{n}}
derivative of y=2e^{2e^x+x}	derivative\:y=2e^{2e^{x}+x}
integral of (x^3+1)/(x(x-1)^3)	\int\:\frac{x^{3}+1}{x(x-1)^{3}}dx
tangent of f(x)=3x^4+2x-1,(2,51)	tangent\:f(x)=3x^{4}+2x-1,(2,51)
integral of (tan(x))^7(sec(x))^2	\int\:(\tan(x))^{7}(\sec(x))^{2}dx
(\partial)/(\partial x)(4ln(xy))	\frac{\partial\:}{\partial\:x}(4\ln(xy))
tangent of x^3-6x^2-34x+40,\at x=6	tangent\:x^{3}-6x^{2}-34x+40,\at\:x=6
integral of-kx	\int\:-kxdx
integral of 1/(x(x+1))	\int\:\frac{1}{x(x+1)}dx
limit as x approaches 0 of ((x+5))/(3x)	\lim\:_{x\to\:0}(\frac{(x+5)}{3x})
derivative of y=(t^2+3)e^t	derivative\:y=(t^{2}+3)e^{t}
tangent of y=3+4x^2-2x^3	tangent\:y=3+4x^{2}-2x^{3}
y^{''}+9y=tsin(5t)	y^{\prime\:\prime\:}+9y=t\sin(5t)
derivative of \sqrt[5]{5x-4}	\frac{d}{dx}(\sqrt[5]{5x-4})
integral of 5e^{2x+e^{2x}}	\int\:5e^{2x+e^{2x}}dx
integral of sqrt(x^2+y^2)	\int\:\sqrt{x^{2}+y^{2}}dx
limit as x approaches 5 of 1/x	\lim\:_{x\to\:5}(\frac{1}{x})
derivative of 1+sin(x)	\frac{d}{dx}(1+\sin(x))
derivative of f(x)=(72)/x	derivative\:f(x)=\frac{72}{x}
derivative of (x+3^2)	\frac{d}{dx}((x+3)^{2})
tangent of 4x^2-5x	tangent\:4x^{2}-5x
integral of (e^{2y})/(e^{2y)-1}	\int\:\frac{e^{2y}}{e^{2y}-1}dy
slope of y^4-4y^2=x^4-9x^2,(3,2)	slope\:y^{4}-4y^{2}=x^{4}-9x^{2},(3,2)

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