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Popular Calculus Problems

integral of (x^4)/(4sqrt(x^2+1))	\int\:\frac{x^{4}}{4\sqrt{x^{2}+1}}dx
integral from 1 to 2 of (x^2+3x^4)	\int\:_{1}^{2}(x^{2}+3x^{4})dx
area x^2+1,x,[-1,2]	area\:x^{2}+1,x,[-1,2]
(d^2)/(dx^2)(3xe^x)	\frac{d^{2}}{dx^{2}}(3xe^{x})
integral of (x-3)/((x-5)x^2)	\int\:\frac{x-3}{(x-5)x^{2}}dx
slope of (1.1)(3.4)	slope\:(1.1)(3.4)
integral from 0 to 1 of x^3x^2	\int\:_{0}^{1}x^{3}x^{2}dx
(\partial)/(\partial x)(e^{-x^4-y^3})	\frac{\partial\:}{\partial\:x}(e^{-x^{4}-y^{3}})
integral from 1 to 1 of x	\int\:_{1}^{1}xdx
derivative of 2x+3x^2	\frac{d}{dx}(2x+3x^{2})
(d^2)/(dx^2)(ln(2x+4))	\frac{d^{2}}{dx^{2}}(\ln(2x+4))
area y=x^2,y=20-x	area\:y=x^{2},y=20-x
integral of csc^2(x/6)	\int\:\csc^{2}(\frac{x}{6})dx
derivative of 2x^{-3}+sqrt(x)-8x+15	\frac{d}{dx}(2x^{-3}+\sqrt{x}-8x+15)
y^{''}+4y=cos(2x)+sin(2x)	y^{\prime\:\prime\:}+4y=\cos(2x)+\sin(2x)
sum from n=0 to infinity of x^{3n}	\sum\:_{n=0}^{\infty\:}x^{3n}
integral of 24e^{20t}	\int\:24e^{20t}dt
integral of 3x^2ln(\sqrt[3]{x-1})	\int\:3x^{2}\ln(\sqrt[3]{x-1})dx
limit as x approaches-3-of 2/(x^2-9)	\lim\:_{x\to\:-3-}(\frac{2}{x^{2}-9})
derivative of y=x^5+cos^5(x)	derivative\:y=x^{5}+\cos^{5}(x)
limit as x approaches 90+of tan(x)	\lim\:_{x\to\:90+}(\tan(x))
(dy)/(dx)+(5/x)y=-x+5	\frac{dy}{dx}+(\frac{5}{x})y=-x+5
partialfraction x/((2x+3))	partialfraction\:\frac{x}{(2x+3)}
derivative of f(x)3x^4(x^2-2x)	derivative\:f(x)3x^{4}(x^{2}-2x)
(\partial)/(\partial x)(2/3 (x^2+1)^{3/2})	\frac{\partial\:}{\partial\:x}(\frac{2}{3}(x^{2}+1)^{\frac{3}{2}})
y^{''}-0.02y=0,y^'(0)=2,y(0)=0	y^{\prime\:\prime\:}-0.02y=0,y^{\prime\:}(0)=2,y(0)=0
derivative of 4^xlog_{7}(sec(x^2))	\frac{d}{dx}(4^{x}\log_{7}(\sec(x^{2})))
limit as x approaches 2 of x^3f(2)	\lim\:_{x\to\:2}(x^{3}f(2))
integral of 2/(xsqrt(x^2-9))	\int\:\frac{2}{x\sqrt{x^{2}-9}}dx
integral from 0 to pi of x^2cos(4x)	\int\:_{0}^{π}x^{2}\cos(4x)dx
derivative of y=3x^{-2}-5x^{-3}+3x^{-1}	derivative\:y=3x^{-2}-5x^{-3}+3x^{-1}
(\partial)/(\partial y)(xtan(y+z))	\frac{\partial\:}{\partial\:y}(x\tan(y+z))
integral of (x^4+1)/(x+1)	\int\:\frac{x^{4}+1}{x+1}dx
integral of 1/((x-1)(x-4))	\int\:\frac{1}{(x-1)(x-4)}dx
integral from 0 to pi of 7e^xsin(x)	\int\:_{0}^{π}7e^{x}\sin(x)dx
derivative of \sqrt[3]{x}*tan(x)	\frac{d}{dx}(\sqrt[3]{x}\cdot\:\tan(x))
tangent of f(x)= 1/(3+2x),\at x=2	tangent\:f(x)=\frac{1}{3+2x},\at\:x=2
integral of (x^2)/(1+x^4)	\int\:\frac{x^{2}}{1+x^{4}}dx
derivative of (cos(sin(x+1))/(tan(1/x)))	\frac{d}{dx}(\frac{\cos(\sin(x+1))}{\tan(\frac{1}{x})})
integral of 1/(sqrt(1-9x^2))	\int\:\frac{1}{\sqrt{1-9x^{2}}}dx
(dy)/(dx)=e^{3x+2y}	\frac{dy}{dx}=e^{3x+2y}
limit as n approaches infinity of n/6 sin(6/n)	\lim\:_{n\to\:\infty\:}(\frac{n}{6}\sin(\frac{6}{n}))
integral from 0 to 1 of (x+1)e^{x^2+2x}	\int\:_{0}^{1}(x+1)e^{x^{2}+2x}dx
integral of e^{tan(5x)}sec^2(5x)	\int\:e^{\tan(5x)}\sec^{2}(5x)dx
(dy)/(dx)=-((x+y)^2)/(2xy+x^2-1)	\frac{dy}{dx}=-\frac{(x+y)^{2}}{2xy+x^{2}-1}
derivative of ((1-2x)/(1+2x))	\frac{d}{dx}(\frac{(1-2x)}{1+2x})
(\partial)/(\partial x)(8x^5y^6+6x^4y^8)	\frac{\partial\:}{\partial\:x}(8x^{5}y^{6}+6x^{4}y^{8})
derivative of 6x^{-4}	derivative\:6x^{-4}
(\partial)/(\partial x)(5y^{1/4}x^{1/2})	\frac{\partial\:}{\partial\:x}(5y^{\frac{1}{4}}x^{\frac{1}{2}})
integral of x^3sqrt(4+x^4)	\int\:x^{3}\sqrt{4+x^{4}}dx
integral of (3\sqrt[4]{x^3}-8x^5+6e^x-2)	\int\:(3\sqrt[4]{x^{3}}-8x^{5}+6e^{x}-2)dx
(dy)/(dx)=y(3-y)	\frac{dy}{dx}=y(3-y)
limit as x approaches+(-1)-of x^2+1	\lim\:_{x\to\:+(-1)-}(x^{2}+1)
derivative of+2x	\frac{d}{dx}(+2x)
tangent of f(x)=6sqrt(x),(9,18)	tangent\:f(x)=6\sqrt{x},(9,18)
f(x)=tan^3(x)	f(x)=\tan^{3}(x)
y^{''}+1y^'+0.25y=0	y^{\prime\:\prime\:}+1y^{\prime\:}+0.25y=0
derivative of ((x-3/(sqrt(2x+1)))^4)	\frac{d}{dx}((\frac{x-3}{\sqrt{2x+1}})^{4})
integral from 12 to 13 of xsqrt(x^2-144)	\int\:_{12}^{13}x\sqrt{x^{2}-144}dx
(\partial)/(\partial x)(xy-ln(xy))	\frac{\partial\:}{\partial\:x}(xy-\ln(xy))
derivative of ((6x^2+4)/((3y^2-4)))	\frac{d}{dx}(\frac{(6x^{2}+4)}{(3y^{2}-4)})
integral from-3 to 0 of 1+sqrt(9-x^2)	\int\:_{-3}^{0}1+\sqrt{9-x^{2}}dx
inverse oflaplace (200)/((s+10)(s+100))	inverselaplace\:\frac{200}{(s+10)(s+100)}
x^{''}-x=0	x^{\prime\:\prime\:}-x=0
derivative of x^3-2x^2+x-20	\frac{d}{dx}(x^{3}-2x^{2}+x-20)
integral from 0 to 1 of xsin(npix)	\int\:_{0}^{1}x\sin(nπx)dx
(\partial)/(\partial y)(y^4)	\frac{\partial\:}{\partial\:y}(y^{4})
derivative of sqrt(sec(x)*x^5)	\frac{d}{dx}(\sqrt{\sec(x)}\cdot\:x^{5})
(\partial)/(\partial x)(x+2y+z)	\frac{\partial\:}{\partial\:x}(x+2y+z)
integral of (12x+30)/(x^2+2x-8)	\int\:\frac{12x+30}{x^{2}+2x-8}dx
limit as x approaches 1 of e^{x^2+7x-8}	\lim\:_{x\to\:1}(e^{x^{2}+7x-8})
(\partial)/(\partial x)(e^{-2y}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-2y}\cos(πx))
integral from-2 to 4 of (x-9)	\int\:_{-2}^{4}(x-9)dx
integral of (x^3+25)/(x^2+25)	\int\:\frac{x^{3}+25}{x^{2}+25}dx
limit as x approaches 2 of 2/(x+2)	\lim\:_{x\to\:2}(\frac{2}{x+2})
derivative of (2x/5)	\frac{d}{dx}(\frac{2x}{5})
y^'=((x^2-y^2))/(xy),y(2)=5	y^{\prime\:}=\frac{(x^{2}-y^{2})}{xy},y(2)=5
derivative of ((3xsin(x)/(3x+1))^3)	\frac{d}{dx}((\frac{3x\sin(x)}{3x+1})^{3})
derivative of y+xy	\frac{d}{dx}(y+xy)
tangent of f(x)=4sec(x),\at (pi/6)	tangent\:f(x)=4\sec(x),\at\:(\frac{π}{6})
f(x)=(sqrt(x-1))/(x+1)	f(x)=\frac{\sqrt{x-1}}{x+1}
(dy)/(dx)=((x-4))/(y+6)	\frac{dy}{dx}=\frac{(x-4)}{y+6}
derivative of f(x)= 1/((x+3)^2)	derivative\:f(x)=\frac{1}{(x+3)^{2}}
derivative of 3x^2-5x	derivative\:3x^{2}-5x
limit as x approaches 0 of \|x+1\|	\lim\:_{x\to\:0}(\left\|x+1\right\|)
integral of (x^3)/(x^2+10x+25)	\int\:\frac{x^{3}}{x^{2}+10x+25}dx
integral of (sqrt(x)+x^{-2})	\int\:(\sqrt{x}+x^{-2})dx
(\partial)/(\partial x)(log_{10}(x+y))	\frac{\partial\:}{\partial\:x}(\log_{10}(x+y))
integral of tsin(9t)	\int\:t\sin(9t)dt
slope of (2.3)(4.4)	slope\:(2.3)(4.4)
(\partial)/(\partial y)(4ysqrt(x))	\frac{\partial\:}{\partial\:y}(4y\sqrt{x})
limit as x approaches 3 of 2/(x^2-9)	\lim\:_{x\to\:3}(\frac{2}{x^{2}-9})
area y=x,4x+y^2=12	area\:y=x,4x+y^{2}=12
inverse oflaplace {5/(s^2+49)}	inverselaplace\:\left\{\frac{5}{s^{2}+49}\right\}
derivative of (a+3y^2+b)^{1/2}	derivative\:(a+3y^{2}+b)^{\frac{1}{2}}
derivative of f(x)=(pi^2)/(x^2+4x)	derivative\:f(x)=\frac{π^{2}}{x^{2}+4x}
integral of-1/27 sin(3x)	\int\:-\frac{1}{27}\sin(3x)dx
integral of (3-5x)/(sqrt(9-5x^2))	\int\:\frac{3-5x}{\sqrt{9-5x^{2}}}dx
derivative of arccos(6/x)	\frac{d}{dx}(\arccos(\frac{6}{x}))
(\partial)/(\partial v)(e^{{u}(v)}+sin(v))	\frac{\partial\:}{\partial\:v}(e^{{u}(v)}+\sin(v))

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