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Popular Calculus Problems

integral of x/((x-1)(x^2+2x+2))	\int\:\frac{x}{(x-1)(x^{2}+2x+2)}dx
derivative of x*e^{2x}	\frac{d}{dx}(x\cdot\:e^{2x})
sum from n=1 to infinity of-30n	\sum\:_{n=1}^{\infty\:}-30n
(\partial)/(\partial t)(cos(xt)+3tx^2)	\frac{\partial\:}{\partial\:t}(\cos(xt)+3tx^{2})
integral of (sin(x))/(cos^2(x)+cos(x)-6)	\int\:\frac{\sin(x)}{\cos^{2}(x)+\cos(x)-6}dx
tangent of f(x)=x^2-3x+5,\at x=1	tangent\:f(x)=x^{2}-3x+5,\at\:x=1
sum from n=0 to infinity of n^3	\sum\:_{n=0}^{\infty\:}n^{3}
tangent of f(x)=-7x^3-8x^2-5x,\at x=-3	tangent\:f(x)=-7x^{3}-8x^{2}-5x,\at\:x=-3
integral of (sin(2x))/(1+cos(2x))	\int\:\frac{\sin(2x)}{1+\cos(2x)}dx
integral from 1 to 2 of e^{1/x}	\int\:_{1}^{2}e^{\frac{1}{x}}dx
integral of ((2y)/((x^2+y^2)^2))	\int\:(\frac{2y}{(x^{2}+y^{2})^{2}})dy
derivative of f(x)=4x^{-3/8}	derivative\:f(x)=4x^{-\frac{3}{8}}
derivative of (x^7/7-x^3-3/x+1/(5x^5))	\frac{d}{dx}(\frac{x^{7}}{7}-x^{3}-\frac{3}{x}+\frac{1}{5x^{5}})
limit as x approaches 0 of (sin(3x^2))/x	\lim\:_{x\to\:0}(\frac{\sin(3x^{2})}{x})
integral of sin(3x)sin(x)	\int\:\sin(3x)\sin(x)dx
integral from-2 to 3 of (4x^2+8)-(3x+2)	\int\:_{-2}^{3}(4x^{2}+8)-(3x+2)dx
integral of 7sqrt(x^5)	\int\:7\sqrt{x^{5}}dx
derivative of 4*(sqrt(x^2+3x))	\frac{d}{dx}(4\cdot\:(\sqrt{x^{2}+3x}))
derivative of 4sec^2(2x)	\frac{d}{dx}(4\sec^{2}(2x))
integral of ((1-sqrt(t))^2)/t	\int\:\frac{(1-\sqrt{t})^{2}}{t}dt
d/(dl)(2pisqrt(l/(9.8)))	\frac{d}{dl}(2π\sqrt{\frac{l}{9.8}})
(dy)/(dx)+y/(x(x+1))=x+1	\frac{dy}{dx}+\frac{y}{x(x+1)}=x+1
integral from 0 to 3 of (3x+2)	\int\:_{0}^{3}(3x+2)dx
integral of tan(x	\int\:\tan(d)xdx
(\partial)/(\partial x)((x+1)^2+2(y-1)^2)	\frac{\partial\:}{\partial\:x}((x+1)^{2}+2(y-1)^{2})
x^2y^'-3xy=4x^6	x^{2}y^{\prime\:}-3xy=4x^{6}
integral of sqrt(16-x)	\int\:\sqrt{16-x}dx
integral of (x^5)/(x^6-4)	\int\:\frac{x^{5}}{x^{6}-4}dx
derivative of csc(xtan(x))	\frac{d}{dx}(\csc(x)\tan(x))
4sin(t)(dy)/(dt)+4ycos(t)=cos(t)sin^4(t)	4\sin(t)\frac{dy}{dt}+4y\cos(t)=\cos(t)\sin^{4}(t)
y^{''}-3y^'+2y=e^{3x}+x^2	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{3x}+x^{2}
limit as x approaches 0 of x^2-2	\lim\:_{x\to\:0}(x^{2}-2)
taylor 3/(x^2-x-2),1	taylor\:\frac{3}{x^{2}-x-2},1
(\partial)/(\partial y)(sqrt(4-x^2-6y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-6y^{2}})
(8t+y+2)dt-dy=0	(8t+y+2)dt-dy=0
integral of x^2sqrt(1+2x)	\int\:x^{2}\sqrt{1+2x}dx
integral of x^2e^{-ax}	\int\:x^{2}e^{-ax}dx
slope ofintercept (3,-29),(-1,7)	slopeintercept\:(3,-29),(-1,7)
y^{''}+6y^'+9y=e^{-3t}	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=e^{-3t}
integral from-infinity to 0 of 1/(5-9x)	\int\:_{-\infty\:}^{0}\frac{1}{5-9x}dx
laplacetransform 3e^{4t}	laplacetransform\:3e^{4t}
4y^{''}-4y^'-3y=cos(2x)	4y^{\prime\:\prime\:}-4y^{\prime\:}-3y=\cos(2x)
d/(da)(tan(a)+cot(a))	\frac{d}{da}(\tan(a)+\cot(a))
8y^{''}+31y=0	8y^{\prime\:\prime\:}+31y=0
(dy)/(dx)=((2x+xy^2))/(4y+yx^2)	\frac{dy}{dx}=\frac{(2x+xy^{2})}{4y+yx^{2}}
(dy}{dx}=\frac{6+3y)/x	\frac{dy}{dx}=\frac{6+3y}{x}
derivative of 2x^4arctan(5x^3)	derivative\:2x^{4}\arctan(5x^{3})
integral of ln^2(2x)	\int\:\ln^{2}(2x)dx
d/(du)(uv)	\frac{d}{du}(uv)
limit as x approaches 0 of-(sin(x))/(3x)	\lim\:_{x\to\:0}(-\frac{\sin(x)}{3x})
integral of xsqrt(x+9)	\int\:x\sqrt{x+9}dx
limit as x approaches-1 of x^2-5x+6	\lim\:_{x\to\:-1}(x^{2}-5x+6)
(\partial)/(\partial y)(3x^2-3y)	\frac{\partial\:}{\partial\:y}(3x^{2}-3y)
integral of ((sqrt(x^2-9)))/(x^3)	\int\:\frac{(\sqrt{x^{2}-9})}{x^{3}}dx
integral of (tan(x)+1)/(tan(x)-1)	\int\:\frac{\tan(x)+1}{\tan(x)-1}dx
(dy)/(dx)y=(9x-6)/(54x^2)	\frac{dy}{dx}y=\frac{9x-6}{54x^{2}}
integral of-(e^{2t})/2	\int\:-\frac{e^{2t}}{2}dt
integral from-1 to 2 of (2x^2-4x+5)	\int\:_{-1}^{2}(2x^{2}-4x+5)dx
(\partial)/(\partial x)(2x^4y-2)	\frac{\partial\:}{\partial\:x}(2x^{4}y-2)
integral of 1/(1+e^{6x)}	\int\:\frac{1}{1+e^{6x}}dx
sum from n=1 to infinity of 5/(n+2)	\sum\:_{n=1}^{\infty\:}\frac{5}{n+2}
integral of (x^3+3)	\int\:(x^{3}+3)dx
e^x(dy)/(dx)=e^{-y}+e^{2x-y}	e^{x}\frac{dy}{dx}=e^{-y}+e^{2x-y}
area cos(x),sin(x)	area\:\cos(x),\sin(x)
2x^2y^{''}+3xy^'=y	2x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}=y
area 2cos(7x),2-2cos(7x),0<= x<= pi/7	area\:2\cos(7x),2-2\cos(7x),0\le\:x\le\:\frac{π}{7}
integral from 0 to 1 of e^{-st}*t	\int\:_{0}^{1}e^{-st}\cdot\:tdt
integral of e^{-4t}	\int\:e^{-4t}dt
(dy)/(dt)=6y+cos(3t)	\frac{dy}{dt}=6y+\cos(3t)
integral of ((t^2+t+1)/((t+3)^3))	\int\:(\frac{t^{2}+t+1}{(t+3)^{3}})dt
-y+10e^{-t}=y^'	-y+10e^{-t}=y^{\prime\:}
integral of ln(6x)	\int\:\ln(6x)dx
laplacetransform sin(2t)+cos(2t)	laplacetransform\:\sin(2t)+\cos(2t)
integral of sin^3(3θ)sqrt(cos(3θ))	\int\:\sin^{3}(3θ)\sqrt{\cos(3θ)}dθ
xy^'+y=-2xy^2,y(1)=-3	xy^{\prime\:}+y=-2xy^{2},y(1)=-3
derivative of 4/(11-x)	\frac{d}{dx}(\frac{4}{11-x})
derivative of y=xsqrt(2x+3)	derivative\:y=x\sqrt{2x+3}
integral of 7^xtan(7^x)	\int\:7^{x}\tan(7^{x})dx
limit as x approaches pi/2 of e^{sin(x)}	\lim\:_{x\to\:\frac{π}{2}}(e^{\sin(x)})
limit as x approaches 0 of (xcos(x))/x	\lim\:_{x\to\:0}(\frac{x\cos(x)}{x})
derivative of 3/(x^2+9)	\frac{d}{dx}(\frac{3}{x^{2}+9})
(\partial)/(\partial y)(ye^{-x^2+y})	\frac{\partial\:}{\partial\:y}(ye^{-x^{2}+y})
integral of (x^2+3)/(xsqrt(x^2-9))	\int\:\frac{x^{2}+3}{x\sqrt{x^{2}-9}}dx
(\partial)/(\partial x)(cos^6(x^8y^6))	\frac{\partial\:}{\partial\:x}(\cos^{6}(x^{8}y^{6}))
area y=2x-x^2,y=2x-4	area\:y=2x-x^{2},y=2x-4
limit as x approaches 9 of ((x^{1/2}-3)(x+1))/(x^2-8x-9)	\lim\:_{x\to\:9}(\frac{(x^{\frac{1}{2}}-3)(x+1)}{x^{2}-8x-9})
derivative of y=(3x^2-2x-4)5^x	derivative\:y=(3x^{2}-2x-4)5^{x}
integral of (5000ln(x+20))/((x+20)^2)	\int\:\frac{5000\ln(x+20)}{(x+20)^{2}}dx
derivative of-5e^{3x}	\frac{d}{dx}(-5e^{3x})
integral of 4\sqrt[6]{x}	\int\:4\sqrt[6]{x}dx
integral of (1+x)/(-4x-2x^2)	\int\:\frac{1+x}{-4x-2x^{2}}dx
derivative of (e^{5x}/(x^{15)})	\frac{d}{dx}(\frac{e^{5x}}{x^{15}})
derivative of b(x+a^3+c)	\frac{d}{dx}(b(x+a)^{3}+c)
(\partial)/(\partial x)(xye^{x/y})	\frac{\partial\:}{\partial\:x}(xye^{\frac{x}{y}})
limit as x approaches infinity of x*2	\lim\:_{x\to\:\infty\:}(x\cdot\:2)
integral of (x^3)/(\sqrt[3]{x^2+5)}	\int\:\frac{x^{3}}{\sqrt[3]{x^{2}+5}}dx
integral from 0 to pi/4 of cos^7(x)	\int\:_{0}^{\frac{π}{4}}\cos^{7}(x)dx
(\partial)/(\partial x)(y^2-4y+xy)	\frac{\partial\:}{\partial\:x}(y^{2}-4y+xy)
derivative of (x^3)/8	derivative\:\frac{x^{3}}{8}
integral of cos^4(6x)	\int\:\cos^{4}(6x)dx

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