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Popular Calculus Problems

integral of 1/(y^2sqrt(14-y^2))	\int\:\frac{1}{y^{2}\sqrt{14-y^{2}}}dy
6(dy)/(dx)+42y=7	6\frac{dy}{dx}+42y=7
derivative of 1/4 (70x^2-8x^3)	derivative\:\frac{1}{4}(70x^{2}-8x^{3})
limit as x approaches-3 of (x+2)/(x^2-9)	\lim\:_{x\to\:-3}(\frac{x+2}{x^{2}-9})
derivative of sqrt((z+1)/(z-1))	derivative\:\sqrt{\frac{z+1}{z-1}}
inverse oflaplace 1/(3s+4)	inverselaplace\:\frac{1}{3s+4}
(\partial)/(\partial x)(z^2(sin(2xy)))	\frac{\partial\:}{\partial\:x}(z^{2}(\sin(2xy)))
integral from 0 to 3 of x/(x^2+6x+13)	\int\:_{0}^{3}\frac{x}{x^{2}+6x+13}dx
integral of 2cos^2(x)tan^3(x)	\int\:2\cos^{2}(x)\tan^{3}(x)dx
e^{kt}((dy)/(dt)+ky)=0	e^{kt}(\frac{dy}{dt}+ky)=0
2x^2yy^'+y^2=2	2x^{2}yy^{\prime\:}+y^{2}=2
tangent of (4x-3)^{1/2}	tangent\:(4x-3)^{\frac{1}{2}}
sum from n=2 to infinity of 3/(n*(n+3))	\sum\:_{n=2}^{\infty\:}\frac{3}{n\cdot\:(n+3)}
limit as n approaches 0 of 1/n sin(1/n)	\lim\:_{n\to\:0}(\frac{1}{n}\sin(\frac{1}{n}))
y^{''}+25y=40sin(5x)	y^{\prime\:\prime\:}+25y=40\sin(5x)
area 2(sqrt(x+6)),-6,-2	area\:2(\sqrt{x+6}),-6,-2
derivative of (x^2+7/(x-3))	\frac{d}{dx}(\frac{x^{2}+7}{x-3})
derivative of 1/(1+9x^2)	derivative\:\frac{1}{1+9x^{2}}
integral of (z^4+10z^3)/(2z^2)	\int\:\frac{z^{4}+10z^{3}}{2z^{2}}dz
derivative of sqrt(x*y)	\frac{d}{dx}(\sqrt{x\cdot\:y})
integral of 2xy^3	\int\:2xy^{3}dx
integral of x^2cos(3x)	\int\:x^{2}\cos(3x)dx
integral of (r^3)/(sqrt(16+r^2))	\int\:\frac{r^{3}}{\sqrt{16+r^{2}}}dr
integral from 0 to 6 of \|x-4\|	\int\:_{0}^{6}\left\|x-4\right\|dx
derivative of ln((x+6^{11}))	\frac{d}{dx}(\ln((x+6)^{11}))
integral from 0 to 0.1 of xarctan(3x)	\int\:_{0}^{0.1}x\arctan(3x)dx
derivative of 200ln(x/(40))	\frac{d}{dx}(200\ln(\frac{x}{40}))
integral of (3t+1)(t-2)	\int\:(3t+1)(t-2)dt
derivative of ln((2x/(x+3)))	\frac{d}{dx}(\ln(\frac{2x}{x+3}))
integral of 1-2cos(x)	\int\:1-2\cos(x)dx
derivative of (13e^{6x})/(x+5)	derivative\:\frac{13e^{6x}}{x+5}
integral of (4x+1)^2	\int\:(4x+1)^{2}dx
integral of 5/(x+4)	\int\:\frac{5}{x+4}dx
derivative of f(x)=(3t-1)/(sqrt(t)-2)	derivative\:f(x)=\frac{3t-1}{\sqrt{t}-2}
integral of-sin(x/a)	\int\:-\sin(\frac{x}{a})dx
limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2)	\lim\:_{(x,y)\to\:(0,0)}(\frac{xy\cos(y)}{3x^{2}+y^{2}})
limit as x approaches 0 of 4	\lim\:_{x\to\:0}(4)
limit as t approaches 0 of e^t	\lim\:_{t\to\:0}(e^{t})
integral from 0 to 3 of x/(sqrt(36-x^2))	\int\:_{0}^{3}\frac{x}{\sqrt{36-x^{2}}}dx
limit as x approaches infinity of an	\lim\:_{x\to\:\infty\:}(an)
derivative of 6\sqrt[4]{x}-5/(x^2)	derivative\:6\sqrt[4]{x}-\frac{5}{x^{2}}
integral of (sqrt(x+36))/x	\int\:\frac{\sqrt{x+36}}{x}dx
integral of csc(θ)cot(θ)	\int\:\csc(θ)\cot(θ)dθ
derivative of f(x)=6sqrt(x)	derivative\:f(x)=6\sqrt{x}
integral of 3x^2sin(x^3)	\int\:3x^{2}\sin(x^{3})dx
(\partial)/(\partial x)(2/(3sqrt(x)))	\frac{\partial\:}{\partial\:x}(\frac{2}{3\sqrt{x}})
derivative of sin(2xcos(x))	\frac{d}{dx}(\sin(2x)\cos(x))
(d^4)/(dx^4)(3e^{x^2})	\frac{d^{4}}{dx^{4}}(3e^{x^{2}})
4y^{''}-4y^'+y=0	4y^{\prime\:\prime\:}-4y^{\prime\:}+y=0
sum from n=1 to infinity of ln(1/(n^2))	\sum\:_{n=1}^{\infty\:}\ln(\frac{1}{n^{2}})
limit as x approaches 3 of (x^2-1)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{2}-1}{x-3})
(dv)/(dt)	\frac{dv}{dt}
y^2(dy)/(dx)=y^3-x^3	y^{2}\frac{dy}{dx}=y^{3}-x^{3}
limit as x approaches pi/2 of f(x)	\lim\:_{x\to\:\frac{π}{2}}(f(x))
derivative of tan^3(4x)	\frac{d}{dx}(\tan^{3}(4x))
tangent of f(x)=-2x^3,(2,-16)	tangent\:f(x)=-2x^{3},(2,-16)
y^{''}+y^'-2y=4sin(2x)	y^{\prime\:\prime\:}+y^{\prime\:}-2y=4\sin(2x)
integral of e^{-0.89x}	\int\:e^{-0.89x}dx
integral of (2y)/1 ^2	\int\:\frac{d^{2}y}{1}dx^{2}
integral of-(6x)/5	\int\:-\frac{6x}{5}dx
derivative of (f(x))^2	derivative\:(f(x))^{2}
laplacetransform 3sin(3t)	laplacetransform\:3\sin(3t)
2x^2yy^'+2xy^2+1=0	2x^{2}yy^{\prime\:}+2xy^{2}+1=0
derivative of 3ln(x+1)	\frac{d}{dx}(3\ln(x+1))
derivative of sqrt(35x)ln(13x)	\frac{d}{dx}(\sqrt{35x}\ln(13x))
derivative of 6x^5-20x^4+20x^3-10x+4	\frac{d}{dx}(6x^{5}-20x^{4}+20x^{3}-10x+4)
integral from 0 to 5 of 1/(x^{18/17)}	\int\:_{0}^{5}\frac{1}{x^{\frac{18}{17}}}dx
limit as x approaches-infinity of 1	\lim\:_{x\to\:-\infty\:}(1)
derivative of 1/5 cos(5x)	\frac{d}{dx}(\frac{1}{5}\cos(5x))
integral of-3x^5	\int\:-3x^{5}dx
derivative of arccot(sqrt(x^2+1))	\frac{d}{dx}(\arccot(\sqrt{x^{2}+1}))
integral of e^{7x+2}	\int\:e^{7x+2}dx
derivative of (3x^2+2^2(x^2-5x)^3)	\frac{d}{dx}((3x^{2}+2)^{2}(x^{2}-5x)^{3})
(\partial)/(\partial x)(6x^2+11y)	\frac{\partial\:}{\partial\:x}(6x^{2}+11y)
integral of 1/(81e^{-5x)+e^{5x}}	\int\:\frac{1}{81e^{-5x}+e^{5x}}dx
integral from 0 to 5 of sqrt(y+4)	\int\:_{0}^{5}\sqrt{y+4}dy
derivative of 2c	derivative\:2c
(dy}{dx}=\frac{5x*sec(y/x)+y)/x	\frac{dy}{dx}=\frac{5x\cdot\:\sec(\frac{y}{x})+y}{x}
(dy)/(dx)+12y=14	\frac{dy}{dx}+12y=14
limit as x approaches 1 of 2x^3-3x^2+x+2	\lim\:_{x\to\:1}(2x^{3}-3x^{2}+x+2)
limit as h approaches 0.1 of (e^h-1)/h	\lim\:_{h\to\:0.1}(\frac{e^{h}-1}{h})
sum from n=0 to infinity of nsin(pi*n)	\sum\:_{n=0}^{\infty\:}n\sin(π\cdot\:n)
simplify ln(7)	simplify\:\ln(7)
derivative of sin(12x)	\frac{d}{dx}(\sin(12x))
integral from 2 to 8 of t^3ln(2t)	\int\:_{2}^{8}t^{3}\ln(2t)dt
area 15-x^2,x^2-3,-3,3	area\:15-x^{2},x^{2}-3,-3,3
derivative of [x+(x+sin^2(x)^6]^5)	\frac{d}{dx}([x+(x+\sin^{2}(x))^{6}]^{5})
(x^2-2y^2)dx+xydy=0	(x^{2}-2y^{2})dx+xydy=0
y^{'''}-6y^{''}=3-cos(x)	y^{\prime\:\prime\:\prime\:}-6y^{\prime\:\prime\:}=3-\cos(x)
limit as x approaches 0-of 1/x-1/(e^x-1)	\lim\:_{x\to\:0-}(\frac{1}{x}-\frac{1}{e^{x}-1})
y^'=10^{x+y}	y^{\prime\:}=10^{x+y}
limit as x approaches 7 of 2x-7	\lim\:_{x\to\:7}(2x-7)
derivative of 6x^4-7x^3+2x+sqrt(2)	\frac{d}{dx}(6x^{4}-7x^{3}+2x+\sqrt{2})
derivative of 6x^{7/2}+4x^{5/2}+2x	\frac{d}{dx}(6x^{\frac{7}{2}}+4x^{\frac{5}{2}}+2x)
derivative of f(x)=sqrt(x)+\sqrt[5]{x}	derivative\:f(x)=\sqrt{x}+\sqrt[5]{x}
inverse oflaplace (e^{-pis})/(s-1)	inverselaplace\:\frac{e^{-πs}}{s-1}
derivative of 2x^6	\frac{d}{dx}(2x^{6})
derivative of-2t(6t^6-1)^6	derivative\:-2t(6t^{6}-1)^{6}
laplacetransform e^{-6t}	laplacetransform\:e^{-6t}
integral of-k/m	\int\:-\frac{k}{m}dt

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