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Popular Calculus Problems

y^'=-y^3,y(0)=-2	y^{\prime\:}=-y^{3},y(0)=-2
(\partial)/(\partial y)(y^2+2xy)	\frac{\partial\:}{\partial\:y}(y^{2}+2xy)
integral of 3e^{5x}	\int\:3e^{5x}dx
sum from n=1 to infinity of n^2*(0.5)^n	\sum\:_{n=1}^{\infty\:}n^{2}\cdot\:(0.5)^{n}
integral from 1 to infinity of 14e^{-7x}	\int\:_{1}^{\infty\:}14e^{-7x}dx
(dy)/(dx)=-8xy^2	\frac{dy}{dx}=-8xy^{2}
(\partial)/(\partial x)(2x^2y+3xy^2)	\frac{\partial\:}{\partial\:x}(2x^{2}y+3xy^{2})
sum from n=1 to infinity of ((-1)/2)^n	\sum\:_{n=1}^{\infty\:}(\frac{-1}{2})^{n}
(\partial)/(\partial x)((4x+4y)e^y)	\frac{\partial\:}{\partial\:x}((4x+4y)e^{y})
laplacetransform 2e^{-t}cos(2t)	laplacetransform\:2e^{-t}\cos(2t)
derivative of (3x^2-2/x)	\frac{d}{dx}(\frac{3x^{2}-2}{x})
sum from n=0 to infinity}((10^{2n of))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(10^{2n})}{n!}
sum from n=1 to infinity of (n/(n+7))^n	\sum\:_{n=1}^{\infty\:}(\frac{n}{n+7})^{n}
integral from 0 to 1 of x*arcsin(x^2)	\int\:_{0}^{1}x\cdot\:\arcsin(x^{2})dx
limit as x approaches+3 of pi	\lim\:_{x\to\:+3}(π)
integral of (6x^3+3x^2-47x-18)/(x^2-9)	\int\:\frac{6x^{3}+3x^{2}-47x-18}{x^{2}-9}dx
limit as x approaches 1 of (arctan(x)-pi/4)/(x-1)	\lim\:_{x\to\:1}(\frac{\arctan(x)-\frac{π}{4}}{x-1})
integral from-r to r of pi(r^2-x^2)	\int\:_{-r}^{r}π(r^{2}-x^{2})dx
tangent of f(x)=7e^{x^2-5x+8},\at x=0	tangent\:f(x)=7e^{x^{2}-5x+8},\at\:x=0
derivative of (3x^2-6x+6)e^{-8x}	derivative\:(3x^{2}-6x+6)e^{-8x}
y(dy)/(dx)=(y^2-y)(2x+5)	y\frac{dy}{dx}=(y^{2}-y)(2x+5)
derivative of sqrt(a^2-y^2)	derivative\:\sqrt{a^{2}-y^{2}}
(x^2+9)y^'+xy=0	(x^{2}+9)y^{\prime\:}+xy=0
d/(dy)(xcos(y))	\frac{d}{dy}(x\cos(y))
integral of (x^3+x^2)/(x^2+5x+6)	\int\:\frac{x^{3}+x^{2}}{x^{2}+5x+6}dx
derivative of (x^2e^x/(x^2+e^x))	\frac{d}{dx}(\frac{x^{2}e^{x}}{x^{2}+e^{x}})
y^{''}-4y^'+4y^'=0	y^{\prime\:\prime\:}-4y^{\prime\:}+4y^{\prime\:}=0
integral of cos^3(x/(12))	\int\:\cos^{3}(\frac{x}{12})dx
limit as x approaches 4+of (x-4)/(x-4)	\lim\:_{x\to\:4+}(\frac{x-4}{x-4})
tangent of 2x^2-9x+10	tangent\:2x^{2}-9x+10
tangent of 2/(x-4)	tangent\:\frac{2}{x-4}
integral from 0 to 3 of 1	\int\:_{0}^{3}1
(\partial)/(\partial z)(x)	\frac{\partial\:}{\partial\:z}(x)
integral from 0 to 4/3 of 1/(16+9x^2)	\int\:_{0}^{\frac{4}{3}}\frac{1}{16+9x^{2}}dx
integral of sin(9x)cos(4x)	\int\:\sin(9x)\cos(4x)dx
integral from 1 to 2 of Inx	\int\:_{1}^{2}Inxdx
y^{''}+2y^'+6y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+6y=0
y^{''}+25y=20sin(5t)	y^{\prime\:\prime\:}+25y=20\sin(5t)
inverse oflaplace 2s	inverselaplace\:2s
(2x+y)dx-xdy=0	(2x+y)dx-xdy=0
(\partial)/(\partial y)(x+y)	\frac{\partial\:}{\partial\:y}(x+y)
(x^2y^4+x^6)dx-x^3y^3dy=0	(x^{2}y^{4}+x^{6})dx-x^{3}y^{3}dy=0
ty^{''}-y^'=0	ty^{\prime\:\prime\:}-y^{\prime\:}=0
(\partial)/(\partial x)((2xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{2xy}{x^{2}+y^{2}})
integral of 3/2 sqrt(t+1)	\int\:\frac{3}{2}\sqrt{t+1}dt
derivative of (5x^2tan(x)/(sec(x)))	\frac{d}{dx}(\frac{5x^{2}\tan(x)}{\sec(x)})
integral from 0 to 1 of (8x^2-5)e^x	\int\:_{0}^{1}(8x^{2}-5)e^{x}dx
(\partial)/(\partial y)(2yt+xj)	\frac{\partial\:}{\partial\:y}(2yt+xj)
integral of (x^2)/(16+x^2)	\int\:\frac{x^{2}}{16+x^{2}}dx
integral of 4t^3y-15t^2-y	\int\:4t^{3}y-15t^{2}-ydt
area 11x-3,10x-5,[12,34]	area\:11x-3,10x-5,[12,34]
integral of 1/(t^2+1)	\int\:\frac{1}{t^{2}+1}dt
limit as x approaches 129 of (x-129)/(sqrt(x+15)-12)	\lim\:_{x\to\:129}(\frac{x-129}{\sqrt{x+15}-12})
derivative of 3^{arctan(x})	\frac{d}{dx}(3^{\arctan(x)})
(\partial)/(\partial x)(xy^2-2y^3+3xz)	\frac{\partial\:}{\partial\:x}(xy^{2}-2y^{3}+3xz)
sum from n=0 to infinity of (n!)/(n^3)	\sum\:_{n=0}^{\infty\:}\frac{n!}{n^{3}}
derivative of (2x+3^{1/2})	\frac{d}{dx}((2x+3)^{\frac{1}{2}})
(\partial)/(\partial x)(3x^2y)	\frac{\partial\:}{\partial\:x}(3x^{2}y)
derivative of sin(x-2)	\frac{d}{dx}(\sin(x-2))
derivative of ((4x-4^5)/((2x-5)^7))	\frac{d}{dx}(\frac{(4x-4)^{5}}{(2x-5)^{7}})
derivative of 38e^{x^2}x	derivative\:38e^{x^{2}}x
integral of 7/(sqrt(5-6x))	\int\:\frac{7}{\sqrt{5-6x}}dx
derivative of 1/2 x^2+2x-2+35x^{-1}	derivative\:\frac{1}{2}x^{2}+2x-2+35x^{-1}
derivative of ln(e^x-e^{-x})	\frac{d}{dx}(\ln(e^{x}-e^{-x}))
derivative of (x^3+2x+3/(x^2))	\frac{d}{dx}(\frac{x^{3}+2x+3}{x^{2}})
integral of y/(sqrt(16+y^2))	\int\:\frac{y}{\sqrt{16+y^{2}}}dy
x^5+y^4sqrt(x^6+4)y^'=0	x^{5}+y^{4}\sqrt{x^{6}+4}y^{\prime\:}=0
(\partial)/(\partial x)(-6e^xcos(yz))	\frac{\partial\:}{\partial\:x}(-6e^{x}\cos(yz))
limit as x approaches 1 of (x^4-6x^2+8x-3)/(x^4-2x^3+2x-1)	\lim\:_{x\to\:1}(\frac{x^{4}-6x^{2}+8x-3}{x^{4}-2x^{3}+2x-1})
integral from 0 to 2 of 2pi(9-x)(8-x^3)	\int\:_{0}^{2}2π(9-x)(8-x^{3})dx
integral from 120 to 150 of 0.1281xe^{-x/(100)}	\int\:_{120}^{150}0.1281\cdot\:x\cdot\:e^{-\frac{x}{100}}dx
4y+y^{''}=0	4y+y^{\prime\:\prime\:}=0
derivative of (1/(x^2)-3/(x^4))(x+9x^3)	derivative\:(\frac{1}{x^{2}}-\frac{3}{x^{4}})(x+9x^{3})
integral of 2/((1+x^2)^2)	\int\:\frac{2}{(1+x^{2})^{2}}dx
(d^2y)/(dt^2)+10(dy)/(dt)+25y=0	\frac{d^{2}y}{dt^{2}}+10\frac{dy}{dt}+25y=0
derivative of (x^3y+xy^3/(x^2+y^2))	\frac{d}{dx}(\frac{x^{3}y+xy^{3}}{x^{2}+y^{2}})
tangent of f(x)=sqrt(x-4),(13,3)	tangent\:f(x)=\sqrt{x-4},(13,3)
tangent of f(x)= 5/(x+1),\at x=(-1)/3	tangent\:f(x)=\frac{5}{x+1},\at\:x=\frac{-1}{3}
limit as x approaches 0 of (0+5)/(3(0))	\lim\:_{x\to\:0}(\frac{0+5}{3(0)})
derivative of f(x)=(x^2+8x+3)/(sqrt(x))	derivative\:f(x)=\frac{x^{2}+8x+3}{\sqrt{x}}
limit as x approaches infinity of (x^2+2x+5)/(e^{3x)}	\lim\:_{x\to\:\infty\:}(\frac{x^{2}+2x+5}{e^{3x}})
derivative of e^xcos(x+e^xsin(x))	\frac{d}{dx}(e^{x}\cos(x)+e^{x}\sin(x))
integral of (sin^2(3x))/(cos(3x))	\int\:\frac{\sin^{2}(3x)}{\cos(3x)}dx
integral of 1/((169-x^2)^{3/2)}	\int\:\frac{1}{(169-x^{2})^{\frac{3}{2}}}dx
taylor 1-x^3	taylor\:1-x^{3}
area 6x^2,x^2+5	area\:6x^{2},x^{2}+5
integral of-1/u	\int\:-\frac{1}{u}du
integral of ((x+4)(x-7))/(x^2)	\int\:\frac{(x+4)(x-7)}{x^{2}}dx
(\partial)/(\partial x)(sqrt((x+5)/(y+4)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x+5}{y+4}})
integral of 1/(9x^2+1)	\int\:\frac{1}{9x^{2}+1}dx
integral of sin(x	\int\:\sin(d)xdx
derivative of (x^3+1/(x^3-1))	\frac{d}{dx}(\frac{x^{3}+1}{x^{3}-1})
integral of (x-1)sqrt(2-x)	\int\:(x-1)\sqrt{2-x}dx
limit as x approaches 3 of (f(x)-f(pi))/(sqrt(x)-\sqrt{3)}	\lim\:_{x\to\:3}(\frac{f(x)-f(π)}{\sqrt{x}-\sqrt{3}})
integral of (sqrt(x)-x+1)/(x^5)	\int\:\frac{\sqrt{x}-x+1}{x^{5}}dx
integral from-infinity to infinity of x^8e^{-x^9}	\int\:_{-\infty\:}^{\infty\:}x^{8}e^{-x^{9}}dx
integral of-4sqrt(x)	\int\:-4\sqrt{x}dx
integral of-cos(x^2)	\int\:-\cos(x^{2})dx
derivative of xsqrt(3+2x^2)	\frac{d}{dx}(x\sqrt{3+2x^{2}})
(1/(ln(x)))^'	(\frac{1}{\ln(x)})^{\prime\:}

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