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Popular Calculus Problems

integral of e^{-x/4}sin(pi/4 x)	\int\:e^{-\frac{x}{4}}\sin(\frac{π}{4}x)dx
integral of ((3x-4))/(x^2-1)	\int\:\frac{(3x-4)}{x^{2}-1}dx
integral from 0 to 4 of pi(16-x^2)	\int\:_{0}^{4}π(16-x^{2})dx
(dy)/(dx)=2(1+y^2)x	\frac{dy}{dx}=2(1+y^{2})x
derivative of arcsin(1/(e^x))	\frac{d}{dx}(\arcsin(\frac{1}{e^{x}}))
derivative of (2+sin(x)/x)	\frac{d}{dx}(\frac{2+\sin(x)}{x})
tangent of f(x)=2x^3-5x,\at x=-1	tangent\:f(x)=2x^{3}-5x,\at\:x=-1
derivative of 1/((t^5+4)^4)	derivative\:\frac{1}{(t^{5}+4)^{4}}
derivative of-ln(x-2)	\frac{d}{dx}(-\ln(x-2))
integral of ((x^2-x+8))/(x^3+2x)	\int\:\frac{(x^{2}-x+8)}{x^{3}+2x}dx
6t((dy)/(dt))+5y=sqrt(t)	6t(\frac{dy}{dt})+5y=\sqrt{t}
(\partial)/(\partial w)(w/(h(w)^2))	\frac{\partial\:}{\partial\:w}(\frac{w}{h(w)^{2}})
derivative of y= 1/(6x-1)	derivative\:y=\frac{1}{6x-1}
integral from 0 to 2 of (x)	\int\:_{0}^{2}(x)dx
integral of sqrt(e^{2θ)+e^{2θ}}	\int\:\sqrt{e^{2θ}+e^{2θ}}dθ
y^{-2}(dy)/(dx)+y^{-1}=2x	y^{-2}\frac{dy}{dx}+y^{-1}=2x
(\partial)/(\partial x)(e^{3x}tan(y))	\frac{\partial\:}{\partial\:x}(e^{3x}\tan(y))
y^{''}+6y^'-16y=0	y^{\prime\:\prime\:}+6y^{\prime\:}-16y=0
(\partial)/(\partial x)(ln(tan(x)))	\frac{\partial\:}{\partial\:x}(\ln(\tan(x)))
limit as x approaches-5-of ((-7x))/(x+5)	\lim\:_{x\to\:-5-}(\frac{(-7x)}{x+5})
integral of 1/(x^3+3x^2+7x+5)	\int\:\frac{1}{x^{3}+3x^{2}+7x+5}dx
integral from 0 to 1 of 2pi(x^5-x^6)	\int\:_{0}^{1}2π(x^{5}-x^{6})dx
derivative of (xy^3+x^2y)^3	derivative\:(xy^{3}+x^{2}y)^{3}
limit as x approaches 4 of sqrt(f(x))	\lim\:_{x\to\:4}(\sqrt{f(x)})
derivative of 1/2 ln(x^2+1)	\frac{d}{dx}(\frac{1}{2}\ln(x^{2}+1))
derivative of f(x)=-4sqrt(x)	derivative\:f(x)=-4\sqrt{x}
y^{''}-5y^'+6y=cos(t)e^{-t}	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=\cos(t)e^{-t}
integral of 10xcos(9x)	\int\:10x\cos(9x)dx
limit as x approaches 0+of (-8)/(3x^{1/7)}	\lim\:_{x\to\:0+}(\frac{-8}{3x^{\frac{1}{7}}})
sum from n=1 to infinity of 4/(n^6)	\sum\:_{n=1}^{\infty\:}\frac{4}{n^{6}}
y=log_{10}(2x-1)	y=\log_{10}(2x-1)
limit as x approaches 0 of (tan(4x))/x	\lim\:_{x\to\:0}(\frac{\tan(4x)}{x})
tangent of f(x)=(sqrt(x))/(3x-8),\at x=2	tangent\:f(x)=\frac{\sqrt{x}}{3x-8},\at\:x=2
y^{''}-5y^'+6.25y=0,y(0)=1,y^'(0)=0.5	y^{\prime\:\prime\:}-5y^{\prime\:}+6.25y=0,y(0)=1,y^{\prime\:}(0)=0.5
limit as x approaches infinity of e^x+1	\lim\:_{x\to\:\infty\:}(e^{x}+1)
integral from pi to 2pi of sin(x)	\int\:_{π}^{2π}\sin(x)dx
derivative of e^{4-x}	\frac{d}{dx}(e^{4-x})
derivative of ln(sin(5x))	\frac{d}{dx}(\ln(\sin(5x)))
derivative of q(x)=(8x-6)^{-1/4}	derivative\:q(x)=(8x-6)^{-\frac{1}{4}}
derivative of Ax^2+Bx+C	\frac{d}{dx}(Ax^{2}+Bx+C)
integral of (x^2)/((x^2+4)(x+2))	\int\:\frac{x^{2}}{(x^{2}+4)(x+2)}dx
expand b+x^2-kln(((x+1)(x-1))/k)-1	expand\:b+x^{2}-k\ln(\frac{(x+1)(x-1)}{k})-1
taylor (2x)/(1+x^2)	taylor\:\frac{2x}{1+x^{2}}
integral of (x+9)/(2x^3-18x)	\int\:\frac{x+9}{2x^{3}-18x}dx
2(dy)/(dx)+18y=9	2\frac{dy}{dx}+18y=9
integral of 5sin^2(3x)	\int\:5\sin^{2}(3x)dx
integral from 0 to 1 of 1/(x^{0.2)}	\int\:_{0}^{1}\frac{1}{x^{0.2}}dx
limit as x approaches 0-of sqrt(x(x-1))	\lim\:_{x\to\:0-}(\sqrt{x(x-1)})
derivative of ((x+1(x+2))/((x-1)(x-2)))	\frac{d}{dx}(\frac{(x+1)(x+2)}{(x-1)(x-2)})
(\partial)/(\partial x)(4x^3+2xy^2+1)	\frac{\partial\:}{\partial\:x}(4x^{3}+2xy^{2}+1)
integral of x^2arctan(4x)	\int\:x^{2}\arctan(4x)dx
derivative of-15	\frac{d}{dx}(-15)
(\partial)/(\partial y)(sin(4y)e^{-5x})	\frac{\partial\:}{\partial\:y}(\sin(4y)e^{-5x})
derivative of (x^7-4x^3+12x/(x^3))	\frac{d}{dx}(\frac{x^{7}-4x^{3}+12x}{x^{3}})
limit as x approaches 0 of 1/(e^x-1)	\lim\:_{x\to\:0}(\frac{1}{e^{x}-1})
slope of (2,-1),(8,4)	slope\:(2,-1),(8,4)
(\partial ^2)/(\partial x^2)(cos(xy))	\frac{\partial\:^{2}}{\partial\:x^{2}}(\cos(xy))
integral from 0 to 4 of 60000te^{-t}	\int\:_{0}^{4}60000te^{-t}dt
integral of x 1/x	\int\:x\frac{1}{x}dx
integral of csc^3(x)cot^5(x)	\int\:\csc^{3}(x)\cot^{5}(x)dx
(\partial)/(\partial x)(yln(x)+xy^2)	\frac{\partial\:}{\partial\:x}(y\ln(x)+xy^{2})
integral of (1/(x^5)-x^5-1/3)	\int\:(\frac{1}{x^{5}}-x^{5}-\frac{1}{3})dx
taylor 2/(1-x^2)	taylor\:\frac{2}{1-x^{2}}
y^{''}-4y^'+4y=0,y(0)=2,y^'(0)=7	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=0,y(0)=2,y^{\prime\:}(0)=7
sum from n=0 to infinity of 1(-1/3)^n	\sum\:_{n=0}^{\infty\:}1(-\frac{1}{3})^{n}
integral of 56x	\int\:56xdx
limit as x approaches 0 of 1/(x+2)-1/2	\lim\:_{x\to\:0}(\frac{1}{x+2}-\frac{1}{2})
derivative of y=4x^{-3}	derivative\:y=4x^{-3}
derivative of 3x^{ln(x})	\frac{d}{dx}(3x^{\ln(x)})
limit as (x,y) approaches (-1,1) of x+y	\lim\:_{(x,y)\to\:(-1,1)}(x+y)
integral from 0 to 1 of (x^3)/(1+x^3)	\int\:_{0}^{1}\frac{x^{3}}{1+x^{3}}dx
d/(dt)(-2cos(t))	\frac{d}{dt}(-2\cos(t))
y^{''}=-ay	y^{\prime\:\prime\:}=-ay
derivative of-2cos(-3x+7)	\frac{d}{dx}(-2\cos(-3x+7))
integral of e^{2x+7}	\int\:e^{2x+7}dx
integral of (2-x)^{1/2}	\int\:(2-x)^{\frac{1}{2}}dx
limit as x approaches 5 of sqrt(6x-4)	\lim\:_{x\to\:5}(\sqrt{6x-4})
integral of 3x^2+2x+1	\int\:3x^{2}+2x+1dx
y^{''}+y=4csc^2(t)	y^{\prime\:\prime\:}+y=4\csc^{2}(t)
limit as x approaches 0 of 1+x	\lim\:_{x\to\:0}(1+x)
derivative of (24/x)	\frac{d}{dx}(\frac{24}{x})
integral from x to x^2 of e^{t^4}	\int\:_{x}^{x^{2}}e^{t^{4}}dt
integral from-1 to 3 of (2x+3)^2	\int\:_{-1}^{3}(2x+3)^{2}dx
derivative of (x-y)/x	derivative\:\frac{x-y}{x}
derivative of (x^2(x+3)/(16(x^2-4)))	\frac{d}{dx}(\frac{x^{2}(x+3)}{16(x^{2}-4)})
(dy)/(dx)=y,y(11)=3	\frac{dy}{dx}=y,y(11)=3
integral of 1/(x^2-x-6)	\int\:\frac{1}{x^{2}-x-6}dx
(\partial)/(\partial x)(-y/x)	\frac{\partial\:}{\partial\:x}(-\frac{y}{x})
tangent of f(x)=((x))/(x-4)	tangent\:f(x)=\frac{(x)}{x-4}
(\partial)/(\partial x)(sin(x^2+5))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}+5))
(8-r^2)dr=r^3sin(θ)dθ	(8-r^{2})dr=r^{3}\sin(θ)dθ
integral from 0 to 1 of (x-6)/(x^2-6x+8)	\int\:_{0}^{1}\frac{x-6}{x^{2}-6x+8}dx
3x(dy)/(dx)=sqrt(x^2-4)	3x\frac{dy}{dx}=\sqrt{x^{2}-4}
limit as x approaches 4 of 2x^2-2x	\lim\:_{x\to\:4}(2x^{2}-2x)
integral from-infinity to 6 of re^{r/2}	\int\:_{-\infty\:}^{6}re^{\frac{r}{2}}dr
(\partial)/(\partial x)(4y^3)	\frac{\partial\:}{\partial\:x}(4y^{3})
(dy)/(dt)=3y+e^{7t}	\frac{dy}{dt}=3y+e^{7t}
derivative of 7(5^x)	derivative\:7(5^{x})
derivative of e^{x+1}-1	\frac{d}{dx}(e^{x+1}-1)
tangent of f(x)=5xcos(x),\at x=pi	tangent\:f(x)=5x\cos(x),\at\:x=π

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