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Popular Calculus Problems

integral from 0 to 8 of te^{-t}	\int\:_{0}^{8}te^{-t}dt
2y^'+y=1	2y^{\prime\:}+y=1
integral from 0 to 2 of x^2(1+2x^3)^3	\int\:_{0}^{2}x^{2}(1+2x^{3})^{3}dx
integral of 5/((x-1)^2)	\int\:\frac{5}{(x-1)^{2}}dx
integral of (x+5)/(2x^3-8x)	\int\:\frac{x+5}{2x^{3}-8x}dx
(\partial)/(\partial x)(cos(x+3y))	\frac{\partial\:}{\partial\:x}(\cos(x+3y))
derivative of 3x^2-2x-1	\frac{d}{dx}(3x^{2}-2x-1)
derivative of sqrt(1-2/x)	\frac{d}{dx}(\sqrt{1-\frac{2}{x}})
integral of sqrt(4-2x^2)	\int\:\sqrt{4-2x^{2}}dx
limit as x approaches 2.99 of x^2+3x	\lim\:_{x\to\:2.99}(x^{2}+3x)
laplacetransform e^8	laplacetransform\:e^{8}
limit as x approaches-4 of x^2-1	\lim\:_{x\to\:-4}(x^{2}-1)
(\partial)/(\partial x)(3x^2+ycos(xy))	\frac{\partial\:}{\partial\:x}(3x^{2}+y\cos(xy))
(\partial)/(\partial x)(sin(2x)cos(8y))	\frac{\partial\:}{\partial\:x}(\sin(2x)\cos(8y))
(d^2)/(dx^2)(sqrt(x^2+21))	\frac{d^{2}}{dx^{2}}(\sqrt{x^{2}+21})
integral from 0 to 3 of (2x-x^2)^4(1-x)	\int\:_{0}^{3}(2x-x^{2})^{4}(1-x)dx
(\partial)/(\partial x)(2xy-18x)	\frac{\partial\:}{\partial\:x}(2xy-18x)
derivative of (3x)/(x^2+1)	derivative\:\frac{3x}{x^{2}+1}
derivative of-x^3+2x+7	\frac{d}{dx}(-x^{3}+2x+7)
inverse oflaplace-5/(s^2+2s+4)	inverselaplace\:-\frac{5}{s^{2}+2s+4}
tangent of x^2-2	tangent\:x^{2}-2
derivative of-1/((x-3^2))	\frac{d}{dx}(-\frac{1}{(x-3)^{2}})
derivative of y=(10)/(ln(x))	derivative\:y=\frac{10}{\ln(x)}
limit as x approaches 0 of (ln(cos(x)))/(ln(cos(2x)))	\lim\:_{x\to\:0}(\frac{\ln(\cos(x))}{\ln(\cos(2x))})
integral of (x-3)^3	\int\:(x-3)^{3}dx
(x^2+1)(dy)/(dx)+5x(y-1)=0,y(0)=4	(x^{2}+1)\frac{dy}{dx}+5x(y-1)=0,y(0)=4
integral of (sin(2x))/(sqrt(1+cos^2(x)))	\int\:\frac{\sin(2x)}{\sqrt{1+\cos^{2}(x)}}dx
(dy)/(dx)=(sec(y))/((x+5)^2)	\frac{dy}{dx}=\frac{\sec(y)}{(x+5)^{2}}
integral of 1/(x^2sqrt(x^2-121))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-121}}dx
derivative of sqrt((1-cx/(1+cx)))	\frac{d}{dx}(\sqrt{\frac{1-cx}{1+cx}})
integral of (x^3)/(sqrt(2-x^2))	\int\:\frac{x^{3}}{\sqrt{2-x^{2}}}dx
(dy)/(dx)= 1/3 x^3	\frac{dy}{dx}=\frac{1}{3}x^{3}
derivative of 13	derivative\:13
integral of sec^2(x)ln(tan(x))	\int\:\sec^{2}(x)\ln(\tan(x))dx
integral of 2tan(4x)	\int\:2\tan(4x)dx
derivative of (xf(x))/5	derivative\:\frac{xf(x)}{5}
integral of ((5x+3))/((x^2-9))	\int\:\frac{(5x+3)}{(x^{2}-9)}dx
(dy)/(dx)=((-y(x+y+1)))/(x+2y)	\frac{dy}{dx}=\frac{(-y(x+y+1))}{x+2y}
integral from-1 to 1 of (1+sqrt(1-x^2))	\int\:_{-1}^{1}(1+\sqrt{1-x^{2}})dx
t^2y^{''}+19ty^'+162y=0	t^{2}y^{\prime\:\prime\:}+19ty^{\prime\:}+162y=0
derivative of 3cos(2u)	derivative\:3\cos(2u)
sum from n=2 to infinity of 1/(n^2+n)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}+n}
derivative of-3e^{1-3x}	\frac{d}{dx}(-3e^{1-3x})
derivative of sqrt(2x+4)	\frac{d}{dx}(\sqrt{2x+4})
(\partial)/(\partial x)(((-y))/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{(-y)}{x^{2}+y^{2}})
y^{''}=ay	y^{\prime\:\prime\:}=ay
y^{'''}-4y^{''}-5y^'=0	y^{\prime\:\prime\:\prime\:}-4y^{\prime\:\prime\:}-5y^{\prime\:}=0
tangent of xy=-100	tangent\:xy=-100
integral of 10x*sqrt(x)	\int\:10x\cdot\:\sqrt{x}dx
derivative of f(x)=3x-8	derivative\:f(x)=3x-8
integral of ((x^2+x+1))/((x+1)^2(x+2))	\int\:\frac{(x^{2}+x+1)}{(x+1)^{2}(x+2)}dx
derivative of y=acsc^2(kx)	derivative\:y=a\csc^{2}(kx)
derivative of \sqrt[3]{3x}	\frac{d}{dx}(\sqrt[3]{3x})
maclaurin 1/((1+x))	maclaurin\:\frac{1}{(1+x)}
((x+1)^2)^'	((x+1)^{2})^{\prime\:}
integral of 1/(x(64x^2-1)^{1/2)}	\int\:\frac{1}{x(64x^{2}-1)^{\frac{1}{2}}}dx
d/(dθ)(9sin(θ))	\frac{d}{dθ}(9\sin(θ))
integral of 16ln(9)	\int\:16\ln(9)
d/(dy)((2xy)/((x^2+y^2)^2))	\frac{d}{dy}(\frac{2xy}{(x^{2}+y^{2})^{2}})
derivative of 9x+1	\frac{d}{dx}(9x+1)
integral from 1 to 3 of 2/((x-2)^{8/3)}	\int\:_{1}^{3}\frac{2}{(x-2)^{\frac{8}{3}}}dx
derivative of 2x^2-5	derivative\:2x^{2}-5
integral from-3 to 3 of x^3	\int\:_{-3}^{3}x^{3}dx
derivative of ln(1+3x+xln(x))	\frac{d}{dx}(\ln(1+3x)+x\ln(x))
derivative of 1/((3x^2+x+2^5))	\frac{d}{dx}(\frac{1}{(3x^{2}+x+2)^{5}})
integral of (-10)/((x-2)(x^2+4))	\int\:\frac{-10}{(x-2)(x^{2}+4)}dx
integral of (tan^4(x))/(sec^5(x))	\int\:\frac{\tan^{4}(x)}{\sec^{5}(x)}dx
y^'=4y^2x	y^{\prime\:}=4y^{2}x
integral of 13tan^5(x)	\int\:13\tan^{5}(x)dx
integral of (t^2)/(1+t^3)	\int\:\frac{t^{2}}{1+t^{3}}dt
integral of (2sqrt(x))/(1+\sqrt[3]{x)}	\int\:\frac{2\sqrt{x}}{1+\sqrt[3]{x}}dx
implicit (dy)/(dx),x^4y-8xy+3xy^2=9	implicit\:\frac{dy}{dx},x^{4}y-8xy+3xy^{2}=9
limit as x approaches 0 of (cos(3x-pi/2))/x	\lim\:_{x\to\:0}(\frac{\cos(3x-\frac{π}{2})}{x})
tangent of f(x)=4x^2-4x+1	tangent\:f(x)=4x^{2}-4x+1
y^{''}+2y^'+2y=sin(x)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(x)
integral of 1/(2sqrt(y-1))	\int\:\frac{1}{2\sqrt{y-1}}dy
sum from n=0 to infinity of 0.9^n	\sum\:_{n=0}^{\infty\:}0.9^{n}
integral of tan^7(x)sec^2(x)	\int\:\tan^{7}(x)\sec^{2}(x)dx
integral from 1 to e of ((x^2+1))/x	\int\:_{1}^{e}\frac{(x^{2}+1)}{x}dx
limit as x approaches 4+of ln(x^2-16)	\lim\:_{x\to\:4+}(\ln(x^{2}-16))
1/2 y^'+y=0,y(1)=1	\frac{1}{2}y^{\prime\:}+y=0,y(1)=1
tangent of f(x)=1-x^2,(1,0)	tangent\:f(x)=1-x^{2},(1,0)
derivative of ((6x^2+6x+8)/(sqrt(x)))	\frac{d}{dx}(\frac{(6x^{2}+6x+8)}{\sqrt{x}})
(\partial)/(\partial y)(xsqrt(1+y^3))	\frac{\partial\:}{\partial\:y}(x\sqrt{1+y^{3}})
laplacetransform 4t*sin(3t)	laplacetransform\:4t\cdot\:\sin(3t)
(xy^')/(y^2)sin(x/y)= 1/y sin(x/y)	\frac{xy^{\prime\:}}{y^{2}}\sin(\frac{x}{y})=\frac{1}{y}\sin(\frac{x}{y})
(\partial)/(\partial y)(sqrt(5x^2+2y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{5x^{2}+2y^{2}})
integral of 13cos^3(x)	\int\:13\cos^{3}(x)dx
(dP)/(dt)= P/5-(P^2)/(75),P(0)=5	\frac{dP}{dt}=\frac{P}{5}-\frac{P^{2}}{75},P(0)=5
derivative of y=-sin(x)	derivative\:y=-\sin(x)
integral of (sqrt(x))/(1+x^2)	\int\:\frac{\sqrt{x}}{1+x^{2}}dx
inverse oflaplace ((e^{-4s}))/(s^2)	inverselaplace\:\frac{(e^{-4s})}{s^{2}}
sum from n=1 to infinity of 3/(n^2+n)	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{2}+n}
integral of (4x^2+6)/(x^3+3x)	\int\:\frac{4x^{2}+6}{x^{3}+3x}dx
derivative of f(x)=sqrt(7x-1)	derivative\:f(x)=\sqrt{7x-1}
y^{''}+4y^'+6y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+6y=0
integral from-1 to 1 of (x^2+1)	\int\:_{-1}^{1}(x^{2}+1)dx
derivative of y=ln((e^x)/(e^x-1))	derivative\:y=\ln(\frac{e^{x}}{e^{x}-1})
tangent of-4x^2-7x	tangent\:-4x^{2}-7x
derivative of f(4)=10x-13	derivative\:f(4)=10x-13

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