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Popular Calculus Problems

area y=x^2,y=4x-x^2	area\:y=x^{2},y=4x-x^{2}
(\partial)/(\partial y)((x+y)^{e^{y^2}})	\frac{\partial\:}{\partial\:y}((x+y)^{e^{y^{2}}})
integral from 0 to 4 of 1/(sqrt(x))	\int\:_{0}^{4}\frac{1}{\sqrt{x}}dx
limit as x approaches infinity of 3x-4	\lim\:_{x\to\:\infty\:}(3x-4)
(2dy)/(dx)-4xy=8x	\frac{2dy}{dx}-4xy=8x
integral of sqrt(x^6-x^8)	\int\:\sqrt{x^{6}-x^{8}}dx
tangent of f(x)=sin(sin(x)),(2pi,0)	tangent\:f(x)=\sin(\sin(x)),(2π,0)
integral of (Inx)/x	\int\:\frac{Inx}{x}dx
integral of (12)/(sec(2x)-1)	\int\:\frac{12}{\sec(2x)-1}dx
integral of 1/(xsqrt(1+2x))	\int\:\frac{1}{x\sqrt{1+2x}}dx
y^'-y=e^{-t}sin(t)	y^{\prime\:}-y=e^{-t}\sin(t)
sum from n=1 to infinity of ln(n^2+2n)	\sum\:_{n=1}^{\infty\:}\ln(n^{2}+2n)
sum from n=1 to infinity of 1/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{7^{n}}
integral of (x-2)^2sin(x)	\int\:(x-2)^{2}\sin(x)dx
integral of 1/(sqrt(x^2+3x-4))	\int\:\frac{1}{\sqrt{x^{2}+3x-4}}dx
y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-7	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=0,y(0)=2,y^{\prime\:}(0)=-7
integral of sin(x)+sec^2(x)+sec(x)tan(x)	\int\:\sin(x)+\sec^{2}(x)+\sec(x)\tan(x)dx
integral of 3/x+x^3	\int\:\frac{3}{x}+x^{3}dx
(\partial)/(\partial x)(4ycos(x))	\frac{\partial\:}{\partial\:x}(4y\cos(x))
(dx)/(dt)=sin(3t)cos(3t)	\frac{dx}{dt}=\sin(3t)\cos(3t)
derivative of x^3-17x^2+63x+6	derivative\:x^{3}-17x^{2}+63x+6
(\partial)/(\partial x)(x^2+y^2+3z)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+3z)
integral of (2x)cos(x)	\int\:(2x)\cos(x)dx
derivative of \sqrt[5]{7x}	derivative\:\sqrt[5]{7x}
taylor tan(x),0,1,2,3, pi/4	taylor\:\tan(x),0,1,2,3,\frac{π}{4}
area y=7x,y=6x^2	area\:y=7x,y=6x^{2}
area x=0,y=2,y=sqrt(x)	area\:x=0,y=2,y=\sqrt{x}
(sin(t)-tcos(t))^'	(\sin(t)-t\cos(t))^{\prime\:}
derivative of (4x/(x+5))	\frac{d}{dx}(\frac{4x}{x+5})
derivative of (1-3x^2(x^2-2)^3)	\frac{d}{dx}((1-3x)^{2}(x^{2}-2)^{3})
(\partial)/(\partial y)(xy+x)	\frac{\partial\:}{\partial\:y}(xy+x)
(dy)/(dx)+y=2	\frac{dy}{dx}+y=2
limit as x approaches-3 of [ 1/2 x^2+3]	\lim\:_{x\to\:-3}([\frac{1}{2}x^{2}+3])
limit as x approaches infinity of a^n	\lim\:_{x\to\:\infty\:}(a^{n})
integral of sin(x^4)	\int\:\sin(x^{4})dx
(\partial)/(\partial z)(2xln(yz))	\frac{\partial\:}{\partial\:z}(2x\ln(yz))
d/(dy)(sin(y^2))	\frac{d}{dy}(\sin(y^{2}))
(\partial)/(\partial x)(nln(θ+2))	\frac{\partial\:}{\partial\:x}(n\ln(θ+2))
integral of x^2-3	\int\:x^{2}-3dx
tangent of f(x)= x/(1+x^2),0,\at x=0	tangent\:f(x)=\frac{x}{1+x^{2}},0,\at\:x=0
derivative of (x^3/3+(x^2)/2-2x+7)	\frac{d}{dx}(\frac{x^{3}}{3}+\frac{x^{2}}{2}-2x+7)
(sec(x))(dy)/(dx)+y=2	(\sec(x))\frac{dy}{dx}+y=2
integral of e^{1x}	\int\:e^{1x}dx
inverse oflaplace (e^{-s})/(s^1)	inverselaplace\:\frac{e^{-s}}{s^{1}}
tangent of f(x)=cos(3x)ln(x^4),(1,0)	tangent\:f(x)=\cos(3x)\ln(x^{4}),(1,0)
derivative of (9x^2/((x^2+x)^3))	\frac{d}{dx}(\frac{9x^{2}}{(x^{2}+x)^{3}})
integral of (sqrt(4-x^2))/(x^4)	\int\:\frac{\sqrt{4-x^{2}}}{x^{4}}dx
derivative of ln(ln(8x))	derivative\:\ln(\ln(8x))
derivative of (-x^3)/(y^3)	derivative\:\frac{-x^{3}}{y^{3}}
area y=4x,y=2x^2	area\:y=4x,y=2x^{2}
derivative of 14x^3+7x^2+11x-29	derivative\:14x^{3}+7x^{2}+11x-29
(dy}{dx}=\frac{4xsec(y/x)+y)/x	\frac{dy}{dx}=\frac{4x\sec(\frac{y}{x})+y}{x}
integral of 1/2 e^{sqrt(5x+6)}	\int\:\frac{1}{2}e^{\sqrt{5x+6}}dx
d/(dt)(5tsin(4pi)t)	\frac{d}{dt}(5t\sin(4π)t)
integral of sin(3x+5)	\int\:\sin(3x+5)dx
(\partial)/(\partial y)(x^2-2y)	\frac{\partial\:}{\partial\:y}(x^{2}-2y)
laplacetransform 4e^{-3t}cos(2t)	laplacetransform\:4e^{-3t}\cos(2t)
limit as t approaches 0 of 9/t-9/(t^2+t)	\lim\:_{t\to\:0}(\frac{9}{t}-\frac{9}{t^{2}+t})
(y-x)y^'=y-x+3	(y-x)y^{\prime\:}=y-x+3
integral of 1/(1+w^2)	\int\:\frac{1}{1+w^{2}}dw
derivative of 2sqrt(\sqrt{1+x^2)+1}	\frac{d}{dx}(2\sqrt{\sqrt{1+x^{2}}+1})
limit as x approaches 3 of ln(x^2-9)	\lim\:_{x\to\:3}(\ln(x^{2}-9))
integral of (5x^2+20x+6)/(x(x+1)^2)	\int\:\frac{5x^{2}+20x+6}{x(x+1)^{2}}dx
integral of x(2x-3)	\int\:x(2x-3)dx
(\partial)/(\partial x)(x^3-6xy+y^3-2)	\frac{\partial\:}{\partial\:x}(x^{3}-6xy+y^{3}-2)
d/(dt)(+6t)	\frac{d}{dt}(+6t)
integral from 4 to 10 of 1/(36+(x-4)^2)	\int\:_{4}^{10}\frac{1}{36+(x-4)^{2}}dx
derivative of \sqrt[6]{x}-6e^x	\frac{d}{dx}(\sqrt[6]{x}-6e^{x})
derivative of sqrt(9+x)	\frac{d}{dx}(\sqrt{9+x})
inverse oflaplace 1/(9s^2+1)	inverselaplace\:\frac{1}{9s^{2}+1}
limit as t approaches 0 of e^{3t}	\lim\:_{t\to\:0}(e^{3t})
tangent of y=5-10x+x^3,\at x=-1	tangent\:y=5-10x+x^{3},\at\:x=-1
derivative of x/(1+e^x)	derivative\:\frac{x}{1+e^{x}}
integral of (5x^2-3)/(x^3-x)	\int\:\frac{5x^{2}-3}{x^{3}-x}dx
tangent of f(x)=sin(pix^2)-pix,\at x=1	tangent\:f(x)=\sin(πx^{2})-πx,\at\:x=1
derivative of y=x^3-8x^2+21x+2	derivative\:y=x^{3}-8x^{2}+21x+2
derivative of y=(90)/(x^5)	derivative\:y=\frac{90}{x^{5}}
2y^'-y=4asin(3t)	2y^{\prime\:}-y=4a\sin(3t)
derivative of G(s)=(8s^2)/(7e^s+s)	derivative\:G(s)=\frac{8s^{2}}{7e^{s}+s}
derivative of ((x^3-6x)^9)/9	derivative\:\frac{(x^{3}-6x)^{9}}{9}
integral of ((x^3))/(1+x^2)	\int\:\frac{(x^{3})}{1+x^{2}}dx
(\partial)/(\partial x)(2x^3y+4)	\frac{\partial\:}{\partial\:x}(2x^{3}y+4)
limit as x approaches 3+of 1/(x-3)	\lim\:_{x\to\:3+}(\frac{1}{x-3})
integral from-infinity to 0 of 1/(5-3x)	\int\:_{-\infty\:}^{0}\frac{1}{5-3x}dx
y^'+ytan(t)=(tan(t))/(cos(t))	y^{\prime\:}+y\tan(t)=\frac{\tan(t)}{\cos(t)}
integral of x^3In(x)	\int\:x^{3}In(x)dx
tangent of e^t+3,\at t=0	tangent\:e^{t}+3,\at\:t=0
y^{''}+4y=sin(t)	y^{\prime\:\prime\:}+4y=\sin(t)
taylor x^{-2},6	taylor\:x^{-2},6
area y^2=x^3,y^2=x	area\:y^{2}=x^{3},y^{2}=x
integral of (-9x^2+2)/(x^3+9x)	\int\:\frac{-9x^{2}+2}{x^{3}+9x}dx
integral of 1/(x^2sqrt(x^2+49))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+49}}dx
derivative of 2/((1-1/3 x^3+1^2))	\frac{d}{dx}(\frac{2}{(1-\frac{1}{3}x^{3}+1)^{2}})
derivative of 5x^2-2x-1	derivative\:5x^{2}-2x-1
integral of (x^2)/(x^4+10x^2+9)	\int\:\frac{x^{2}}{x^{4}+10x^{2}+9}dx
y^{''}+4y^'+4y=e^{-2x}ln(x)	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{-2x}\ln(x)
derivative of f(x)= 1/(7-x)	derivative\:f(x)=\frac{1}{7-x}
derivative of h(sqrt(x))	\frac{d}{dx}(h(\sqrt{x}))
derivative of f(x)= 9/(sqrt(x))	derivative\:f(x)=\frac{9}{\sqrt{x}}
(dy)/(dx)= 1/6 sqrt(y)cos^2(sqrt(y))	\frac{dy}{dx}=\frac{1}{6}\sqrt{y}\cos^{2}(\sqrt{y})

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