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Popular Calculus Problems

integral from 1 to 2 of 18x^24^{x^3}	\int\:_{1}^{2}18x^{2}4^{x^{3}}dx
integral of (x^2)/(sqrt(x+1))	\int\:\frac{x^{2}}{\sqrt{x+1}}dx
limit as x approaches 0-of 1+e^{1/x}	\lim\:_{x\to\:0-}(1+e^{\frac{1}{x}})
laplacetransform 3t^2+15t+15	laplacetransform\:3t^{2}+15t+15
slope of y=(5x^2-1)^{-3}	slope\:y=(5x^{2}-1)^{-3}
integral from-infinity to 0 of xe^{8x}	\int\:_{-\infty\:}^{0}xe^{8x}dx
derivative of 2x^2-4x	derivative\:2x^{2}-4x
(\partial)/(\partial z)(-z)	\frac{\partial\:}{\partial\:z}(-z)
integral of 1/((x-2)(x-3))	\int\:\frac{1}{(x-2)(x-3)}dx
integral from-3 to 3 of (18)/(x^2-6x-72)	\int\:_{-3}^{3}\frac{18}{x^{2}-6x-72}dx
(\partial)/(\partial y)((2x)/((2x+3y)^2))	\frac{\partial\:}{\partial\:y}(\frac{2x}{(2x+3y)^{2}})
derivative of f(x)=e^t	derivative\:f(x)=e^{t}
tangent of y=sqrt(2x+1),(4,3)	tangent\:y=\sqrt{2x+1},(4,3)
integral of (x^2)/(e^{x/3)}	\int\:\frac{x^{2}}{e^{\frac{x}{3}}}dx
laplacetransform 5*t	laplacetransform\:5\cdot\:t
integral of 1/(x^2sqrt(x^2+25))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+25}}dx
(\partial)/(\partial y)(sqrt(x/y))	\frac{\partial\:}{\partial\:y}(\sqrt{\frac{x}{y}})
derivative of (4083)/(1+6.22e^{-0.32x)}	derivative\:\frac{4083}{1+6.22e^{-0.32x}}
derivative of f(x)= 4/3 pir^3	derivative\:f(x)=\frac{4}{3}πr^{3}
integral of 24x^2(6-5x^3)^7	\int\:24x^{2}(6-5x^{3})^{7}dx
tangent of f(x)= x/(sqrt(9+x^2)),\at x=0	tangent\:f(x)=\frac{x}{\sqrt{9+x^{2}}},\at\:x=0
y^{''}+2y^'+2y=sin(5t)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(5t)
x^2(dy)/(dx)-2xy=3y^4,y(1)= 1/2	x^{2}\frac{dy}{dx}-2xy=3y^{4},y(1)=\frac{1}{2}
integral of ln(8x)	\int\:\ln(8x)dx
derivative of sin(5x-3)	derivative\:\sin(5x-3)
integral of 9x^2\sqrt[4]{7+4x^3}	\int\:9x^{2}\sqrt[4]{7+4x^{3}}dx
(\partial)/(\partial x)(ysin(y/x))	\frac{\partial\:}{\partial\:x}(y\sin(\frac{y}{x}))
limit as x approaches-4 of 5x+2	\lim\:_{x\to\:-4}(5x+2)
limit as x approaches-2 of ((3))/((x+2))	\lim\:_{x\to\:-2}(\frac{(3)}{(x+2)})
integral from 0 to 6 of pi/4 (36-y^2)	\int\:_{0}^{6}\frac{π}{4}(36-y^{2})dy
integral from 0 to 1 of 34.6e^{-0.06t}	\int\:_{0}^{1}34.6e^{-0.06t}dt
integral from 0 to 0.15 of x	\int\:_{0}^{0.15}xdx
limit as x approaches 0 of x^9cos(4/x)	\lim\:_{x\to\:0}(x^{9}\cos(\frac{4}{x}))
integral of 1/(xsqrt(49x^4-4))	\int\:\frac{1}{x\sqrt{49x^{4}-4}}dx
y^{''}-y^'-2y=te^{2t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=te^{2t}
derivative of-1/9 (x^{-9}-x^{18})	derivative\:-\frac{1}{9}(x^{-9}-x^{18})
derivative of 3sqrt(x)+8	\frac{d}{dx}(3\sqrt{x}+8)
t((dy)/(dt))=2te^t-y+6t^2	t(\frac{dy}{dt})=2te^{t}-y+6t^{2}
integral from 0 to 2pi of sin^2(t)	\int\:_{0}^{2π}\sin^{2}(t)dt
(\partial)/(\partial x)(25x^{(3/4)}y^{1/4})	\frac{\partial\:}{\partial\:x}(25x^{(\frac{3}{4})}y^{\frac{1}{4}})
y^'+(2(y-1))/x =0	y^{\prime\:}+\frac{2(y-1)}{x}=0
integral from 0 to 1 of sqrt(e^{2x)}	\int\:_{0}^{1}\sqrt{e^{2x}}dx
area 15-x^2,x^2-3	area\:15-x^{2},x^{2}-3
sum from n=1 to infinity of 2e^{-9n}	\sum\:_{n=1}^{\infty\:}2e^{-9n}
integral of te^{8t}	\int\:te^{8t}dt
derivative of f(x)=5x^{-3/5}	derivative\:f(x)=5x^{-\frac{3}{5}}
tangent of y=x^3-7x^2+8x+1	tangent\:y=x^{3}-7x^{2}+8x+1
2y^{''}+y^'-4y=0,y(0)=0,y^'(0)=1	2y^{\prime\:\prime\:}+y^{\prime\:}-4y=0,y(0)=0,y^{\prime\:}(0)=1
(\partial)/(\partial y)(xe^{xy})	\frac{\partial\:}{\partial\:y}(x\cdot\:e^{x\cdot\:y})
(\partial)/(\partial x)(-x/((x^2+y^2)))	\frac{\partial\:}{\partial\:x}(-\frac{x}{(x^{2}+y^{2})})
y^{''}-2y^'+y=8e^x	y^{\prime\:\prime\:}-2y^{\prime\:}+y=8e^{x}
limit as x approaches 0+of (ln(x))^2	\lim\:_{x\to\:0+}((\ln(x))^{2})
derivative of sec^2(x)+tan^2(x)	derivative\:\sec^{2}(x)+\tan^{2}(x)
tangent of f(x)=15x-1.86x^2,\at x=a	tangent\:f(x)=15x-1.86x^{2},\at\:x=a
derivative of 7^{x^2}	\frac{d}{dx}(7^{x^{2}})
integral of-3x^2-20x+2000	\int\:-3x^{2}-20x+2000dx
(1+x^2)(dy)/(dx)-(4x^3y)/(1-x^2)=1	(1+x^{2})\frac{dy}{dx}-\frac{4x^{3}y}{1-x^{2}}=1
integral of 3x^2+8x-9	\int\:3x^{2}+8x-9dx
(\partial)/(\partial x)(ln(t+2cx))	\frac{\partial\:}{\partial\:x}(\ln(t+2cx))
derivative of f(x)=ax^b+de^{-cx}	derivative\:f(x)=ax^{b}+de^{-cx}
integral of (4^x-sec^2(x))	\int\:(4^{x}-\sec^{2}(x))dx
integral of 1 (e^{-x}y)	\int\:\frac{d}{1}(e^{-x}y)dx
(dy)/(dx)=(x+y^2)/(2y),y(0)=1	\frac{dy}{dx}=\frac{x+y^{2}}{2y},y(0)=1
integral of (x^5)/(x^6-7)	\int\:\frac{x^{5}}{x^{6}-7}dx
limit as θ approaches 0 of 1/11	\lim\:_{θ\to\:0}(\frac{1}{11})
laplacetransform sin^2(x)	laplacetransform\:\sin^{2}(x)
derivative of (x+2sqrt(x)e^x)	\frac{d}{dx}((x+2\sqrt{x})e^{x})
derivative of (sin(x)/(2x))	\frac{d}{dx}(\frac{\sin(x)}{2x})
integral from-3 to 3 of sqrt(9-x^2)	\int\:_{-3}^{3}\sqrt{9-x^{2}}dx
integral from-2 to 2 of (x^2-4)^2	\int\:_{-2}^{2}(x^{2}-4)^{2}dx
integral of (e^{2x}*,x)	\int\:(e^{2x}\cdot\:,x)dx
derivative of (8*sqrt(x))/(x^2+p)	derivative\:\frac{8\cdot\:\sqrt{x}}{x^{2}+p}
integral of e^x*e^x	\int\:e^{x}\cdot\:e^{x}dx
sum from n=1 to infinity of 4/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{4}{5^{n}}
derivative of 6x+8/3	derivative\:6x+\frac{8}{3}
integral of (ln^2(5))/(2x)	\int\:\frac{\ln^{2}(5)}{2x}dx
derivative of-3x^2cos(3x)	derivative\:-3x^{2}\cos(3x)
integral of ((ax)^3+e^{-bx})	\int\:((ax)^{3}+e^{-bx})dx
integral from 0 to 2 of x^3(7-x^2)^{1/2}	\int\:_{0}^{2}x^{3}(7-x^{2})^{\frac{1}{2}}dx
integral from 0 to 4 of (x^2-4x+3)	\int\:_{0}^{4}(x^{2}-4x+3)dx
4t(dy)/(dt)-5y=sqrt(t)	4t\frac{dy}{dt}-5y=\sqrt{t}
integral of-2*3^{6x}	\int\:-2\cdot\:3^{6x}dx
derivative of y=cot^2(x)	derivative\:y=\cot^{2}(x)
(\partial)/(\partial x)(sqrt(x^2+y^2)-z)	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}}-z)
limit as x approaches 3 of pi	\lim\:_{x\to\:3}(π)
xy^'+2y=5sqrt(x)	xy^{\prime\:}+2y=5\sqrt{x}
(\partial)/(\partial x)(t/(x+1))	\frac{\partial\:}{\partial\:x}(\frac{t}{x+1})
integral from-2pi to pi of sin^2(x)	\int\:_{-2π}^{π}\sin^{2}(x)dx
limit as x approaches 3 of (ln(x)-ln(3))/(x-3)	\lim\:_{x\to\:3}(\frac{\ln(x)-\ln(3)}{x-3})
(\partial)/(\partial x)(z^3x)	\frac{\partial\:}{\partial\:x}(z^{3}x)
integral of 5sec(x+3)tan(x+3)	\int\:5\sec(x+3)\tan(x+3)dx
xy^'+3y=4x,y(3)=6	xy^{\prime\:}+3y=4x,y(3)=6
(\partial)/(\partial x)(x^3-6xy+y^3)	\frac{\partial\:}{\partial\:x}(x^{3}-6xy+y^{3})
(\partial)/(\partial z)(z^3-x^2y)	\frac{\partial\:}{\partial\:z}(z^{3}-x^{2}y)
y^'=(2t)/(y+t^2y)	y^{\prime\:}=\frac{2t}{y+t^{2}y}
limit as n approaches infinity of 1/(n!)	\lim\:_{n\to\:\infty\:}(\frac{1}{n!})
limit as x approaches 0 of 1/(x^2(x+8))	\lim\:_{x\to\:0}(\frac{1}{x^{2}(x+8)})
y^{''}+4y=sin(2x)	y^{\prime\:\prime\:}+4y=\sin(2x)
integral from 0 to 8 of \sqrt[3]{x}	\int\:_{0}^{8}\sqrt[3]{x}dx
(dy)/(dx)+4y^2=0	\frac{dy}{dx}+4y^{2}=0

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