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Popular Calculus Problems

area y=sqrt(x),y= 1/4 x+1,x=0	area\:y=\sqrt{x},y=\frac{1}{4}x+1,x=0
integral of xycos(xy)	\int\:xy\cos(xy)dx
(dy)/(dx)=(y-y^2)	\frac{dy}{dx}=(y-y^{2})
integral of e^{2/t}	\int\:e^{\frac{2}{t}}dt
integral of sin^3(5x)sqrt(cos(5x))	\int\:\sin^{3}(5x)\sqrt{\cos(5x)}dx
integral from 1 to sqrt(2 of)x3^{(x^2)}	\int\:_{1}^{\sqrt{2}}x3^{(x^{2})}dx
(x^2+y^2)dx+xydy=0	(x^{2}+y^{2})dx+xydy=0
(\partial)/(\partial x)(-ysin(xln(y))ln(y))	\frac{\partial\:}{\partial\:x}(-y\sin(x\ln(y))\ln(y))
limit as x approaches e of-11-12	\lim\:_{x\to\:e}(-11-12)
derivative of y=sqrt(x+12)	derivative\:y=\sqrt{x+12}
2x-1+(3y+7)(dy)/(dx)=0	2x-1+(3y+7)\frac{dy}{dx}=0
integral of 1/(2x)-2/(x^2)+3/(sqrt(x))	\int\:\frac{1}{2x}-\frac{2}{x^{2}}+\frac{3}{\sqrt{x}}dx
integral of (cos(x))/(1+sin(x))	\int\:\frac{\cos(x)}{1+\sin(x)}dx
derivative of sqrt(x^2+36)	\frac{d}{dx}(\sqrt{x^{2}+36})
integral of (-3x+2)/(x^3+x^2-2)	\int\:\frac{-3x+2}{x^{3}+x^{2}-2}dx
integral of (3/(u^2)+4/(u^3)-2)	\int\:(\frac{3}{u^{2}}+\frac{4}{u^{3}}-2)du
y^{''}-4y^'=sin(3x)	y^{\prime\:\prime\:}-4y^{\prime\:}=\sin(3x)
derivative of 7x^6-4x^5	derivative\:7x^{6}-4x^{5}
integral of cos(2x)+sin(x)	\int\:\cos(2x)+\sin(x)dx
integral of 10000-x^2	\int\:10000-x^{2}dx
area y=x^2-4x,y=-2x	area\:y=x^{2}-4x,y=-2x
limit as x approaches 2 of-2x^2	\lim\:_{x\to\:2}(-2x^{2})
area 4x^2,sqrt(1/4 x)	area\:4x^{2},\sqrt{\frac{1}{4}x}
derivative of tanh(ln(x))	\frac{d}{dx}(\tanh(\ln(x)))
integral of 1/(sqrt(x^2-a))	\int\:\frac{1}{\sqrt{x^{2}-a}}dx
derivative of e^{9x^2}+x	\frac{d}{dx}(e^{9x^{2}}+x)
inverse oflaplace (3se^{-s})/(2s^2+8)	inverselaplace\:\frac{3se^{-s}}{2s^{2}+8}
limit as x approaches 2-of-2/(sqrt(2-x))	\lim\:_{x\to\:2-}(-\frac{2}{\sqrt{2-x}})
-2y^'+(4y)/x =x^4y^3	-2y^{\prime\:}+\frac{4y}{x}=x^{4}y^{3}
(\partial)/(\partial x)(x^3-3xy^2)	\frac{\partial\:}{\partial\:x}(x^{3}-3xy^{2})
derivative of 2/(1-x^2)	\frac{d}{dx}(\frac{2}{1-x^{2}})
integral of 1/(2x-1)	\int\:\frac{1}{2x-1}dx
derivative of (5sqrt(1-x^3)/6)	\frac{d}{dx}(\frac{5\sqrt{1-x^{3}}}{6})
integral of 13arctan(sqrt(x))	\int\:13\arctan(\sqrt{x})dx
limit as x approaches+0 of (e^{2x}-1)/(sin(3x))	\lim\:_{x\to\:+0}(\frac{e^{2x}-1}{\sin(3x)})
limit as x approaches 3 of x^3-2x^2+1	\lim\:_{x\to\:3}(x^{3}-2x^{2}+1)
sum from n=1 to infinity of (30)/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{30}{3^{n}}
area y= 2/(1+x^2),y=\|x\|	area\:y=\frac{2}{1+x^{2}},y=\left\|x\right\|
integral of (2x)/(sqrt(4-x^2))	\int\:\frac{2x}{\sqrt{4-x^{2}}}dx
integral of 4e^{7x}	\int\:4e^{7x}dx
(dy)/(dx)=x^4y^{-7}	\frac{dy}{dx}=x^{4}y^{-7}
derivative of 2x^2-3x+3	\frac{d}{dx}(2x^{2}-3x+3)
limit as x approaches 0 of 2x-1	\lim\:_{x\to\:0}(2x-1)
derivative of (sin(5x))^{ln(x)}	derivative\:(\sin(5x))^{\ln(x)}
y'=2y-3y^2	y\prime\:=2y-3y^{2}
derivative of x/(x^2+81)	derivative\:\frac{x}{x^{2}+81}
derivative of arctan((x-1/x))	\frac{d}{dx}(\arctan(\frac{x-1}{x}))
integral of tan(x)sec^2(x)	\int\:\tan(x)\sec^{2}(x)dx
integral of 1/2 sin((2pit)/5)	\int\:\frac{1}{2}\sin(\frac{2πt}{5})dt
integral of (1+x)^{-2}	\int\:(1+x)^{-2}dx
integral of 8/(t^2(t^2-4))	\int\:\frac{8}{t^{2}(t^{2}-4)}dt
limit as x approaches 2 of 5x^2-4x+3	\lim\:_{x\to\:2}(5x^{2}-4x+3)
tangent of y=9x-4x^2,(-2,-34)	tangent\:y=9x-4x^{2},(-2,-34)
integral of (cos(pi/(x^5)))/(x^6)	\int\:\frac{\cos(\frac{π}{x^{5}})}{x^{6}}dx
integral of sin(ln(x))	\int\:\sin(\ln(x))dx
integral of 0.5x	\int\:0.5xdx
y^{''}+9y=cos(3x)	y^{\prime\:\prime\:}+9y=\cos(3x)
limit as x approaches-8 of x(8)	\lim\:_{x\to\:-8}(x(8))
derivative of 1/x-ln(x)	\frac{d}{dx}(\frac{1}{x}-\ln(x))
(\partial)/(\partial z)(tan(3+2x^2y^3z^2))	\frac{\partial\:}{\partial\:z}(\tan(3+2x^{2}y^{3}z^{2}))
tangent of (2x+1)^{1/5},\at x=2	tangent\:(2x+1)^{\frac{1}{5}},\at\:x=2
sum from n=0 to infinity of n/((n^2+3))	\sum\:_{n=0}^{\infty\:}\frac{n}{(n^{2}+3)}
d/(dy)(2xy)	\frac{d}{dy}(2xy)
derivative of f(x)=-(12)/(s^5)	derivative\:f(x)=-\frac{12}{s^{5}}
derivative of 4/3 pi*r^2	derivative\:\frac{4}{3}π\cdot\:r^{2}
y^{''}-4y^'+5y=36cos(3t)-28sin(3t)	y^{\prime\:\prime\:}-4y^{\prime\:}+5y=36\cos(3t)-28\sin(3t)
limit as x approaches 3 of 2x^2+5x-7	\lim\:_{x\to\:3}(2x^{2}+5x-7)
derivative of 1/2 cos^4(5x)	\frac{d}{dx}(\frac{1}{2}\cos^{4}(5x))
d/(dy)(1-x^2y)	\frac{d}{dy}(1-x^{2}y)
limit as n approaches infinity of 9	\lim\:_{n\to\:\infty\:}(9)
derivative of-12x^2-16x+16	\frac{d}{dx}(-12x^{2}-16x+16)
derivative of x^{9/10}	\frac{d}{dx}(x^{\frac{9}{10}})
(dP)/(dt)+2tP=P+4t-2	\frac{dP}{dt}+2tP=P+4t-2
sum from n=1 to infinity of n^5(1+n^6)^5	\sum\:_{n=1}^{\infty\:}n^{5}(1+n^{6})^{5}
derivative of (x^{-2}+x^{-3}(x^5-2x^2))	\frac{d}{dx}((x^{-2}+x^{-3})(x^{5}-2x^{2}))
integral of cos^5(2y)	\int\:\cos^{5}(2y)dy
derivative of cos(x^{-3})	\frac{d}{dx}(\cos(x^{-3}))
slope ofintercept (-4,-4),(2,5)	slopeintercept\:(-4,-4),(2,5)
area f(x)=x,g(x)=sqrt(x)	area\:f(x)=x,g(x)=\sqrt{x}
f^'(x)=(9x-2)/(8x+7)	f^{\prime\:}(x)=\frac{9x-2}{8x+7}
derivative of axe^{-2x}	\frac{d}{dx}(axe^{-2x})
(dy)/(dx)=(x+1)/(e^{3y+9)}	\frac{dy}{dx}=\frac{x+1}{e^{3y+9}}
limit as x approaches 2 of (10-3x)^2	\lim\:_{x\to\:2}((10-3x)^{2})
integral from 1 to 36 of e^{sqrt(x)}	\int\:_{1}^{36}e^{\sqrt{x}}dx
area y= 9/(sqrt(9x-x^2)),x=1,x=7.5	area\:y=\frac{9}{\sqrt{9x-x^{2}}},x=1,x=7.5
integral from-1 to 1 of 2-x^2	\int\:_{-1}^{1}2-x^{2}dx
integral from-1 to 2 of x^2-2x	\int\:_{-1}^{2}x^{2}-2xdx
taylor (1+x)^n0	taylor\:(1+x)^{n}0
derivative of (2x^2-3x/(x-2))	\frac{d}{dx}(\frac{2x^{2}-3x}{x-2})
(\partial)/(\partial x)(6y+1)	\frac{\partial\:}{\partial\:x}(6y+1)
limit as x approaches 0-of sin(pi/x)	\lim\:_{x\to\:0-}(\sin(\frac{π}{x}))
(\partial)/(\partial x)((e^{-x/2})(4x^2))	\frac{\partial\:}{\partial\:x}((e^{-\frac{x}{2}})(4x^{2}))
derivative of f(x)=2x-5x^{3/4}	derivative\:f(x)=2x-5x^{\frac{3}{4}}
integral from 3 to infinity of 6/(x^2-x)	\int\:_{3}^{\infty\:}\frac{6}{x^{2}-x}dx
(\partial)/(\partial y)(x^2-xy^2+4y^5)	\frac{\partial\:}{\partial\:y}(x^{2}-xy^{2}+4y^{5})
(\partial)/(\partial y)(sin(x)cos(y))	\frac{\partial\:}{\partial\:y}(\sin(x)\cos(y))
derivative of 3/(x^2+2)	\frac{d}{dx}(\frac{3}{x^{2}+2})
d/(d{x)}({x}-2{y}+2{z})	\frac{d}{d{x}}({x}-2{y}+2{z})
integral of 3/(sqrt(1+x^2))	\int\:\frac{3}{\sqrt{1+x^{2}}}dx
inverse oflaplace 1/((s-1)^2+1)	inverselaplace\:\frac{1}{(s-1)^{2}+1}

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