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Popular Calculus Problems

area sqrt(x),x-2,0	area\:\sqrt{x},x-2,0
(\partial)/(\partial x)(ln(x^2-4xy+y^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}-4xy+y^{2}))
limit as x approaches 0 of 4/(17+x)	\lim\:_{x\to\:0}(\frac{4}{17+x})
integral of 1/((x^2+9))	\int\:\frac{1}{(x^{2}+9)}dx
derivative of x^2+sqrt(x)	\frac{d}{dx}(x^{2}+\sqrt{x})
derivative of (1/(x^2-2/(x^4))(x+8x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{2}{x^{4}})(x+8x^{3}))
sum from n=1 to infinity of (1/2)^{1/n}	\sum\:_{n=1}^{\infty\:}(\frac{1}{2})^{\frac{1}{n}}
integral from 1 to 2 of (x+1/x)^2	\int\:_{1}^{2}(x+\frac{1}{x})^{2}dx
(\partial)/(\partial y)(5x^2-3xy+xyz)	\frac{\partial\:}{\partial\:y}(5x^{2}-3xy+xyz)
limit as x approaches infinity of-2*x	\lim\:_{x\to\:\infty\:}(-2\cdot\:x)
area y=e^{-x},x=2,y=1	area\:y=e^{-x},x=2,y=1
derivative of arccos(x/pi)	\frac{d}{dx}(\arccos(\frac{x}{π}))
integral of sec^2(x)-6	\int\:\sec^{2}(x)-6dx
(\partial)/(\partial y)(3x^2y^4+1)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{4}+1)
(\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1)	\frac{\partial\:}{\partial\:x}(4x^{3}y^{2}-4x^{2}+y^{6}+1)
integral from 2 to 6 of x^2	\int\:_{2}^{6}x^{2}dx
(\partial)/(\partial y)(3x^2-3y^2)	\frac{\partial\:}{\partial\:y}(3x^{2}-3y^{2})
(\partial)/(\partial x)(sqrt(9-2x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{9-2x^{2}-y^{2}})
integral of 1/4 sin(2x)	\int\:\frac{1}{4}\sin(2x)dx
integral of x^3sqrt(x^4+11)	\int\:x^{3}\sqrt{x^{4}+11}dx
integral of 2sin(x/2)	\int\:2\sin(\frac{x}{2})dx
integral of (65x+7)/((8x+1)(x-1))	\int\:\frac{65x+7}{(8x+1)(x-1)}dx
integral of (sin(x)*cos(x))	\int\:(\sin(x)\cdot\:\cos(x))dx
y^{''}-2y^'+y=3e^{2x}	y^{\prime\:\prime\:}-2y^{\prime\:}+y=3e^{2x}
tangent of y= 4/x ,(-5,-4/5)	tangent\:y=\frac{4}{x},(-5,-\frac{4}{5})
7sqrt(xy)(dy)/(dx)=1	7\sqrt{xy}\frac{dy}{dx}=1
slope of (-5,-7),(4,-1)	slope\:(-5,-7),(4,-1)
tangent of sqrt(x),\at x=81	tangent\:\sqrt{x},\at\:x=81
derivative of e^r	derivative\:e^{r}
(y^3-t^3)dt-ty^2dy=0,y(1)=3	(y^{3}-t^{3})dt-ty^{2}dy=0,y(1)=3
f(x)=(5-4x^2+x^5)/(x^3)	f(x)=\frac{5-4x^{2}+x^{5}}{x^{3}}
(dy)/(dx)=8xsqrt(25-y^2)	\frac{dy}{dx}=8x\sqrt{25-y^{2}}
sum from n=1 to infinity of 3-2/(3^n)	\sum\:_{n=1}^{\infty\:}3-\frac{2}{3^{n}}
integral from b to 2b of x^7	\int\:_{b}^{2b}x^{7}dx
limit as h approaches+0 of h	\lim\:_{h\to\:+0}(h)
integral of 2xy^2-3	\int\:2xy^{2}-3dx
integral of 1/(x^2sqrt(x^2-8))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-8}}dx
(\partial)/(\partial y)(ln(x^2+3xy))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+3xy))
f(x)=x^2e^x	f(x)=x^{2}e^{x}
integral of xsqrt(81-x^2)	\int\:x\sqrt{81-x^{2}}dx
integral from 0 to 12 of 2pix(12x-x^2)	\int\:_{0}^{12}2πx(12x-x^{2})dx
derivative of (u-u)(u+u)	derivative\:(u-u)(u+u)
derivative of x^2+2x-3	derivative\:x^{2}+2x-3
x^2y^'=2x^2e^{4x}-3xy	x^{2}y^{\prime\:}=2x^{2}e^{4x}-3xy
d/(dt)((cos(t)+sin(t))/(-sin(t)+cos(t)))	\frac{d}{dt}(\frac{\cos(t)+\sin(t)}{-\sin(t)+\cos(t)})
integral of (26)/(sqrt(x)+x\sqrt{x)}	\int\:\frac{26}{\sqrt{x}+x\sqrt{x}}dx
limit as x approaches 0 of (x+2)^2	\lim\:_{x\to\:0}((x+2)^{2})
tangent of x^4-25x^2+144	tangent\:x^{4}-25x^{2}+144
integral of x^2(-cos(x))'	\int\:x^{2}(-\cos(x))\prime\:dx
derivative of \sqrt[4]{7x}	\frac{d}{dx}(\sqrt[4]{7x})
derivative of 370*2^{(1/10 x)}	derivative\:370\cdot\:2^{(\frac{1}{10}x)}
integral of x/((5x+2)^3)	\int\:\frac{x}{(5x+2)^{3}}dx
integral of 1/(sqrt(x-1)+\sqrt{x+1)}	\int\:\frac{1}{\sqrt{x-1}+\sqrt{x+1}}dx
integral of e^{-x}ln(x)	\int\:e^{-x}\ln(x)dx
tangent of y=3x^2-5x,(2,2)	tangent\:y=3x^{2}-5x,(2,2)
derivative of ln(x/(1-x))	\frac{d}{dx}(\ln(\frac{x}{1-x}))
integral of (x+sin(y))	\int\:(x+\sin(y))dx
derivative of f(x)=2x^2-9	derivative\:f(x)=2x^{2}-9
integral of (x/6)^n	\int\:(\frac{x}{6})^{n}dx
integral from 0 to ln(4) of e^x-e^{-4x}	\int\:_{0}^{\ln(4)}e^{x}-e^{-4x}dx
(\partial)/(\partial x)(x^2ye^{x^2+y^2})	\frac{\partial\:}{\partial\:x}(x^{2}ye^{x^{2}+y^{2}})
integral of sqrt((x-1)/(x^5))	\int\:\sqrt{\frac{x-1}{x^{5}}}dx
(1+x^4)dy=-x(1+4y^2)dx	(1+x^{4})dy=-x(1+4y^{2})dx
limit as x approaches 0 of 1/x*sin(x)	\lim\:_{x\to\:0}(\frac{1}{x}\cdot\:\sin(x))
y^'=xy	y^{\prime\:}=xy
derivative of 7x^2-12x	\frac{d}{dx}(7x^{2}-12x)
derivative of sqrt(3/2 x-5)	\frac{d}{dx}(\sqrt{\frac{3}{2}x-5})
derivative of \sqrt[9]{x^8}-x^pi	derivative\:\sqrt[9]{x^{8}}-x^{π}
limit as x approaches 0 of (\|6x\|)/(3x)	\lim\:_{x\to\:0}(\frac{\left\|6x\right\|}{3x})
derivative of 7x^2-4x	\frac{d}{dx}(7x^{2}-4x)
derivative of f(x)=(x^5-5x^2)/(2x^5+5x)	derivative\:f(x)=\frac{x^{5}-5x^{2}}{2x^{5}+5x}
(\partial)/(\partial x)(3xz^3e^{y^2})	\frac{\partial\:}{\partial\:x}(3xz^{3}e^{y^{2}})
integral of (ln(2x))^2	\int\:(\ln(2x))^{2}dx
limit as x approaches-3 of 2/(x+2)	\lim\:_{x\to\:-3}(\frac{2}{x+2})
integral of x(sqrt(x+3))	\int\:x(\sqrt{x+3})dx
derivative of x/(x-6)	derivative\:\frac{x}{x-6}
derivative of f(x)=(x^3+1)e^x	derivative\:f(x)=(x^{3}+1)e^{x}
integral from 1 to 3 of (x^2+2x-2)	\int\:_{1}^{3}(x^{2}+2x-2)dx
integral of x^2(4x+7)	\int\:x^{2}(4x+7)dx
derivative of 20xe^{-x}	\frac{d}{dx}(20xe^{-x})
(\partial)/(\partial y)(2y^2sqrt(x))	\frac{\partial\:}{\partial\:y}(2y^{2}\sqrt{x})
laplacetransform sin(2t)cos(2t)	laplacetransform\:\sin(2t)\cos(2t)
slope of (1950,53700),(2000,142000)	slope\:(1950,53700),(2000,142000)
derivative of f(x)=\sqrt[3]{x},x=27	derivative\:f(x)=\sqrt[3]{x},x=27
y^'=(64xy)^{1/3}	y^{\prime\:}=(64xy)^{\frac{1}{3}}
derivative of y= x/2	derivative\:y=\frac{x}{2}
derivative of 9/(x^3)	derivative\:\frac{9}{x^{3}}
integral of ((3x^2+7x+3))/(x(x+1)^2)	\int\:\frac{(3x^{2}+7x+3)}{x(x+1)^{2}}dx
(\partial)/(\partial x)((sin(y))/(x^2+1))	\frac{\partial\:}{\partial\:x}(\frac{\sin(y)}{x^{2}+1})
integral of sqrt(10x-x^2)	\int\:\sqrt{10x-x^{2}}dx
inverse oflaplace 3/((s^2+9))	inverselaplace\:\frac{3}{(s^{2}+9)}
taylor 1/x ,-1	taylor\:\frac{1}{x},-1
integral of (3x^5)/(sqrt(5-12x^6))	\int\:\frac{3x^{5}}{\sqrt{5-12x^{6}}}dx
integral from 1 to e of 2/x	\int\:_{1}^{e}\frac{2}{x}dx
integral of (-1)^n	\int\:(-1)^{n}
(\partial)/(\partial x)(tan(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\tan(x^{2}+y^{2}))
f(x)=-8sin(4x)-0.4e^{-0.2x}	f(x)=-8\sin(4x)-0.4e^{-0.2x}
limit as x approaches-9 of 8/(x+9)	\lim\:_{x\to\:-9}(\frac{8}{x+9})
(\partial)/(\partial y)(xy+2x-ln(x^2y))	\frac{\partial\:}{\partial\:y}(xy+2x-\ln(x^{2}y))
integral from 0 to 1 of (sin(pix))^2	\int\:_{0}^{1}(\sin(πx))^{2}dx

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