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Popular Calculus Problems

integral of 3/(sqrt(e^x))	\int\:\frac{3}{\sqrt{e^{x}}}dx
derivative of f(x)=2^{x^2}	derivative\:f(x)=2^{x^{2}}
integral from 0 to 4 of pi((y^2)/2)^2	\int\:_{0}^{4}π(\frac{y^{2}}{2})^{2}dy
integral from 3 to 5 of 1/(4+(x-3)^2)	\int\:_{3}^{5}\frac{1}{4+(x-3)^{2}}dx
y^'+3y=e^xy^2	y^{\prime\:}+3y=e^{x}y^{2}
limit as x approaches 4+of (x+5)/(x-4)	\lim\:_{x\to\:4+}(\frac{x+5}{x-4})
9y^{''}+y=0	9y^{\prime\:\prime\:}+y=0
y^{''}+4y=t^2+3e^t	y^{\prime\:\prime\:}+4y=t^{2}+3e^{t}
integral from 0 to pi of cos^6(x)	\int\:_{0}^{π}\cos^{6}(x)dx
y^'=0.285(1-y)	y^{\prime\:}=0.285(1-y)
100y^{''}=0	100y^{\prime\:\prime\:}=0
limit as x approaches 3 of 5x^2	\lim\:_{x\to\:3}(5x^{2})
derivative of x^{-2/3}(x+5)	\frac{d}{dx}(x^{-\frac{2}{3}}(x+5))
derivative of (6x+8x^2/((3+8x)^2))	\frac{d}{dx}(\frac{6x+8x^{2}}{(3+8x)^{2}})
derivative of f(x)=sqrt(2x^2+1)	derivative\:f(x)=\sqrt{2x^{2}+1}
integral of (8e^{2x})/(e^{2x)+3e^x+2}	\int\:\frac{8e^{2x}}{e^{2x}+3e^{x}+2}dx
derivative of 6cos(x)csc(x^2)	derivative\:6\cos(x)\csc(x^{2})
laplacetransform cos(3t+5)	laplacetransform\:\cos(3t+5)
limit as x approaches-2+of 2x+sqrt(2+x)	\lim\:_{x\to\:-2+}(2x+\sqrt{2+x})
tangent of x^2+x+4	tangent\:x^{2}+x+4
y^{''}-3y^'+7y=4e^{3t}	y^{\prime\:\prime\:}-3y^{\prime\:}+7y=4e^{3t}
derivative of (8.7x+0.2/(x^2-4.5x+7.5))	\frac{d}{dx}(\frac{8.7x+0.2}{x^{2}-4.5x+7.5})
limit as x approaches 1 of \sqrt[3]{x-1}	\lim\:_{x\to\:1}(\sqrt[3]{x-1})
limit as x approaches 0+of (ln(x))/(1/x)	\lim\:_{x\to\:0+}(\frac{\ln(x)}{\frac{1}{x}})
tangent of f(x)=x^3-3x-5,\at x=1	tangent\:f(x)=x^{3}-3x-5,\at\:x=1
(\partial)/(\partial x)(ln(x+6y+8z))	\frac{\partial\:}{\partial\:x}(\ln(x+6y+8z))
(dy)/(dx)=-2/(x^3)+2e^{2x-2}	\frac{dy}{dx}=-\frac{2}{x^{3}}+2e^{2x-2}
tangent of f(x)=2x^2+5x^2-2,\at x=2	tangent\:f(x)=2x^{2}+5x^{2}-2,\at\:x=2
slope of y=x^2+6	slope\:y=x^{2}+6
integral from-1 to 1 of \|x^3-x\|	\int\:_{-1}^{1}\left\|x^{3}-x\right\|dx
integral of (sin^2(x))/4	\int\:\frac{\sin^{2}(x)}{4}dx
integral from 0 to infinity of sin^2(x)	\int\:_{0}^{\infty\:}\sin^{2}(x)dx
limit as x approaches 5 of (3x^2-x-2)0	\lim\:_{x\to\:5}((3x^{2}-x-2)0)
derivative of f(x)=arccsc(2x^4-5)	derivative\:f(x)=\arccsc(2x^{4}-5)
integral from 1 to 2 of ((x-4)^2)/(x^5)	\int\:_{1}^{2}\frac{(x-4)^{2}}{x^{5}}dx
slope of (11/8 ,-1/2),(1/4 , 1/4)	slope\:(\frac{11}{8},-\frac{1}{2}),(\frac{1}{4},\frac{1}{4})
limit as x approaches 0 of (sin(3))/(2x)	\lim\:_{x\to\:0}(\frac{\sin(3)}{2x})
normal of y=3x^2,(-4,48)	normal\:y=3x^{2},(-4,48)
integral of (x^2+3)/(x^2+1)	\int\:\frac{x^{2}+3}{x^{2}+1}dx
limit as x approaches-3 of 3x+9	\lim\:_{x\to\:-3}(3x+9)
simplify 3/4 x^{4/3}-3/8 x^{2/3}+7	simplify\:\frac{3}{4}x^{\frac{4}{3}}-\frac{3}{8}x^{\frac{2}{3}}+7
6y^{''}-y^'-y=0,y(0)=10,y^'(0)=3	6y^{\prime\:\prime\:}-y^{\prime\:}-y=0,y(0)=10,y^{\prime\:}(0)=3
derivative of (x-sqrt(x)/(x+sqrt(x)))	\frac{d}{dx}(\frac{x-\sqrt{x}}{x+\sqrt{x}})
integral of (1+cos(x))/2	\int\:\frac{1+\cos(x)}{2}dx
sum from n=3 to infinity of-5/(n^{1.01)}	\sum\:_{n=3}^{\infty\:}-\frac{5}{n^{1.01}}
derivative of f(x)=7x^3-5x+8	derivative\:f(x)=7x^{3}-5x+8
derivative of cos(3t)	derivative\:\cos(3t)
derivative of (10x/((x^2+1)^2))	\frac{d}{dx}(\frac{10x}{(x^{2}+1)^{2}})
(dy)/(dt)=(t+y)^2-1	\frac{dy}{dt}=(t+y)^{2}-1
limit as x approaches 5 of sqrt(9-x^2)	\lim\:_{x\to\:5}(\sqrt{9-x^{2}})
integral of y/(y+3)	\int\:\frac{y}{y+3}dy
limit as x approaches 0 of (5x^2)/(x^4)	\lim\:_{x\to\:0}(\frac{5x^{2}}{x^{4}})
integral from 0 to 2 of x^3sqrt(3x+1)	\int\:_{0}^{2}x^{3}\sqrt{3x+1}dx
taylor ln(x),\at 4	taylor\:\ln(x),\at\:4
f(x)=(-x(x+4))/((x^2-x-2)^2)	f(x)=\frac{-x(x+4)}{(x^{2}-x-2)^{2}}
sum from n=1 to infinity of ((e^n))/n	\sum\:_{n=1}^{\infty\:}\frac{(e^{n})}{n}
y^{'''}+13y^{''}-9y^'-405y=0	y^{\prime\:\prime\:\prime\:}+13y^{\prime\:\prime\:}-9y^{\prime\:}-405y=0
y^'=3-(2y)/(200+x)	y^{\prime\:}=3-\frac{2y}{200+x}
integral of (2+x)/(9+x^2)	\int\:\frac{2+x}{9+x^{2}}dx
integral of 2/((25+x^2)^{3/2)}	\int\:\frac{2}{(25+x^{2})^{\frac{3}{2}}}dx
integral of 1/6 sin(6x)	\int\:\frac{1}{6}\sin(6x)dx
y^{''}+ay^'+by=0	y^{\prime\:\prime\:}+ay^{\prime\:}+by=0
integral of xsqrt(a^2-x^2)	\int\:x\sqrt{a^{2}-x^{2}}dx
derivative of f(x)=sqrt((x^2*7^x)^7)	derivative\:f(x)=\sqrt{(x^{2}\cdot\:7^{x})^{7}}
limit as x approaches infinity of (sin(2x))/x	\lim\:_{x\to\:\infty\:}(\frac{\sin(2x)}{x})
area x=4y-8,x=sqrt(4y+1)	area\:x=4y-8,x=\sqrt{4y+1}
integral of 1/(x*ln^2(x))	\int\:\frac{1}{x\cdot\:\ln^{2}(x)}dx
integral of 3cot(x)	\int\:3\cot(x)dx
integral of sin(1/4 x)	\int\:\sin(\frac{1}{4}x)dx
(\partial)/(\partial x)((x-u)^2)	\frac{\partial\:}{\partial\:x}((x-u)^{2})
limit as x approaches 3 of (x-3)^2	\lim\:_{x\to\:3}((x-3)^{2})
derivative of e^{-3x^4}*ln(7x^2)	\frac{d}{dx}(e^{-3x^{4}}\cdot\:\ln(7x^{2}))
(\partial)/(\partial y)(x/(y^2))	\frac{\partial\:}{\partial\:y}(\frac{x}{y^{2}})
limit as x approaches 0 of 7/(1+x)	\lim\:_{x\to\:0}(\frac{7}{1+x})
derivative of 3x^2-x^4	\frac{d}{dx}(3x^{2}-x^{4})
integral of ((2x^3+10x^2+8x-12)/(4x))	\int\:(\frac{2x^{3}+10x^{2}+8x-12}{4x})dx
integral of x/(x^2+9)	\int\:\frac{x}{x^{2}+9}dx
y^{'''}+2y^{''}-10y^'-20y=0	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}-10y^{\prime\:}-20y=0
derivative of f(x)=x^2+x-7	derivative\:f(x)=x^{2}+x-7
limit as x approaches 2 of x^2-3x+4	\lim\:_{x\to\:2}(x^{2}-3x+4)
derivative of (x^6/(5-x^5))	\frac{d}{dx}(\frac{x^{6}}{5-x^{5}})
area x=9y^2,x=20+4y^2	area\:x=9y^{2},x=20+4y^{2}
derivative of sqrt(x)+\sqrt[5]{x}+1/7	\frac{d}{dx}(\sqrt{x}+\sqrt[5]{x}+\frac{1}{7})
limit as x approaches infinity of e	\lim\:_{x\to\:\infty\:}(e)
integral from 0 to 1 of (x+6)(x-7)	\int\:_{0}^{1}(x+6)(x-7)dx
integral of (2520x)\sqrt[3]{5+3x}	\int\:(2520x)\sqrt[3]{5+3x}dx
(d^2)/(dx^2)((1-4x)/(1+4x))	\frac{d^{2}}{dx^{2}}(\frac{1-4x}{1+4x})
(dy)/(dx)=(e^x)/(y+2)	\frac{dy}{dx}=\frac{e^{x}}{y+2}
(\partial)/(\partial x)(x^2-7x+12)	\frac{\partial\:}{\partial\:x}(x^{2}-7x+12)
integral of x/(sqrt(x^4-16))	\int\:\frac{x}{\sqrt{x^{4}-16}}dx
x^2y^{''}-7xy^'+12y=0	x^{2}y^{\prime\:\prime\:}-7xy^{\prime\:}+12y=0
integral of x/(cos^2(x^2))	\int\:\frac{x}{\cos^{2}(x^{2})}dx
integral of x^2sin(xz)	\int\:x^{2}\sin(xz)dz
limit as x approaches 0 of (sqrt(x+2)-2)/(sqrt(2x+5)-3)	\lim\:_{x\to\:0}(\frac{\sqrt{x+2}-2}{\sqrt{2x+5}-3})
integral of cos(x)*sin^3(x)	\int\:\cos(x)\cdot\:\sin^{3}(x)dx
derivative of 1/(x^2cos(x))	\frac{d}{dx}(\frac{1}{x^{2}\cos(x)})
y^'=135yx^4	y^{\prime\:}=135yx^{4}
derivative of f(x)=(5x^3+2)(3x^3+2)	derivative\:f(x)=(5x^{3}+2)(3x^{3}+2)
sum from n=1 to infinity of (n-1)/(9n-1)	\sum\:_{n=1}^{\infty\:}\frac{n-1}{9n-1}
laplacetransform e^{-t}(t^2+4t+5)	laplacetransform\:e^{-t}(t^{2}+4t+5)

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