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Popular Calculus Problems

limit as v approaches 4 of (v^2-6v+8)/(2v^2-8v)	\lim\:_{v\to\:4}(\frac{v^{2}-6v+8}{2v^{2}-8v})
integral of (2x)/(sqrt(25-x^2))	\int\:\frac{2x}{\sqrt{25-x^{2}}}dx
integral of 8/(sqrt(x^2+16))	\int\:\frac{8}{\sqrt{x^{2}+16}}dx
integral of 1/(6y^2)	\int\:\frac{1}{6y^{2}}dy
integral from a to b of x(b-x)^2	\int\:_{a}^{b}x(b-x)^{2}dx
(dy)/(dx)=2y-y^2	\frac{dy}{dx}=2y-y^{2}
derivative of 2x^7-3x^6+3x^3-4x^2-7	\frac{d}{dx}(2x^{7}-3x^{6}+3x^{3}-4x^{2}-7)
integral of (7-7x)/(1-sqrt(x))	\int\:\frac{7-7x}{1-\sqrt{x}}dx
integral of x(x^2-1)^3	\int\:x(x^{2}-1)^{3}dx
derivative of f(x)=2-3x	derivative\:f(x)=2-3x
y^'-3y=xy^{-4}	y^{\prime\:}-3y=xy^{-4}
derivative of T\sqrt[4]{7/9}	derivative\:T\sqrt[4]{\frac{7}{9}}
slope ofintercept (3.1)(4.2)	slopeintercept\:(3.1)(4.2)
derivative of (e^x/(6x^2+5))	\frac{d}{dx}(\frac{e^{x}}{6x^{2}+5})
(\partial)/(\partial x)(x^2+y^2+x^2y+9)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+x^{2}y+9)
derivative of f(x)=(xe^{2x-4})	derivative\:f(x)=(xe^{2x-4})
integral of sin^3(xco)s^{-2}x	\int\:\sin^{3}(xco)s^{-2}xdx
derivative of sqrt(7-x)	derivative\:\sqrt{7-x}
derivative of sin^5(x)	derivative\:\sin^{5}(x)
integral of (x+3)/(sqrt(4-(x-2)^2))	\int\:\frac{x+3}{\sqrt{4-(x-2)^{2}}}dx
derivative of 2^{90}	derivative\:2^{90}
derivative of f(x)=2x^2-7x+5	derivative\:f(x)=2x^{2}-7x+5
derivative of-2xsin(2x)	\frac{d}{dx}(-2x\sin(2x))
derivative of f(t)=cos(t)	derivative\:f(t)=\cos(t)
(\partial)/(\partial x)(x^2y^3+4xyz-3yz)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}+4xyz-3yz)
laplacetransform 6e^{-3}-t^2+2t-8	laplacetransform\:6e^{-3}-t^{2}+2t-8
xy^'+2y=-2sin(x)	xy^{\prime\:}+2y=-2\sin(x)
integral of 10sin^3(xco)s^7x	\int\:10\sin^{3}(xco)s^{7}xdx
simplify (4x)/(sqrt(x))	simplify\:\frac{4x}{\sqrt{x}}
integral of x/(sqrt(2x-6))	\int\:\frac{x}{\sqrt{2x-6}}dx
derivative of (cx^{1/2})	\frac{d}{dx}((cx)^{\frac{1}{2}})
limit as t approaches 2-of-(3t)/(t-2)	\lim\:_{t\to\:2-}(-\frac{3t}{t-2})
derivative of 11x^2e^x	derivative\:11x^{2}e^{x}
sum from n=0 to infinity of (e^n)/((n!))	\sum\:_{n=0}^{\infty\:}\frac{e^{n}}{(n!)}
integral of (e^{4x})	\int\:(e^{4x})dx
(dN)/(dt)+N=Nte^{t+3}	\frac{dN}{dt}+N=Nte^{t+3}
derivative of sqrt(5x+6)	derivative\:\sqrt{5x+6}
integral of (1-sqrt(x))/(1+sqrt(x))	\int\:\frac{1-\sqrt{x}}{1+\sqrt{x}}dx
derivative of 1/(2sqrt(x))+1/(3x^{2/3)}	derivative\:\frac{1}{2\sqrt{x}}+\frac{1}{3x^{\frac{2}{3}}}
derivative of (8x^3-6x^2/(x^2+3x-2))	\frac{d}{dx}(\frac{8x^{3}-6x^{2}}{x^{2}+3x-2})
integral from 2 to 4 of 1/(sqrt(16-t^2))	\int\:_{2}^{4}\frac{1}{\sqrt{16-t^{2}}}dt
limit as x approaches 2 of 2x-2	\lim\:_{x\to\:2}(2x-2)
integral of (sec(sqrt(x)))/(sqrt(x))	\int\:\frac{\sec(\sqrt{x})}{\sqrt{x}}dx
y^{''}-2y^'-3y=-3te^{-t}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=-3te^{-t}
integral of x^2sin(4x)	\int\:x^{2}\sin(4x)dx
derivative of 7sec(x)	derivative\:7\sec(x)
derivative of (ln(1-x^2)/(x^2))	\frac{d}{dx}(\frac{\ln(1-x^{2})}{x^{2}})
integral of (cot(ln(x^4+1))x^3)/(x^4+1)	\int\:\frac{\cot(\ln(x^{4}+1))x^{3}}{x^{4}+1}dx
integral of 1/(x^2+12)	\int\:\frac{1}{x^{2}+12}dx
area 3x,9x^2	area\:3x,9x^{2}
sum from n=1 to infinity of (2n)/(11^n)	\sum\:_{n=1}^{\infty\:}\frac{2n}{11^{n}}
derivative of (4sqrt(2)/3 x^{3/2}-1)	\frac{d}{dx}(\frac{4\sqrt{2}}{3}x^{\frac{3}{2}}-1)
derivative of (1-x^{2/3})^{3/2}	derivative\:(1-x^{\frac{2}{3}})^{\frac{3}{2}}
integral of 3x^2y+4xy^2	\int\:3x^{2}y+4xy^{2}dx
integral of \sqrt[7]{tan(8x)}sec^2(8x)	\int\:\sqrt[7]{\tan(8x)}\sec^{2}(8x)dx
integral of x+6	\int\:x+6dx
integral of tln(t)	\int\:t\ln(t)dt
(\partial)/(\partial x)(ln(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}-y^{2}))
integral of 1/(x^2+2x+50)	\int\:\frac{1}{x^{2}+2x+50}dx
limit as x approaches pi/2 of cos(x)	\lim\:_{x\to\:\frac{π}{2}}(\cos(x))
integral of sin(xy)	\int\:\sin(xy)dx
derivative of e^{7x}	derivative\:e^{7x}
limit as x approaches 1 of (x^4-1)/(x^3-1)	\lim\:_{x\to\:1}(\frac{x^{4}-1}{x^{3}-1})
integral of (8-e^x)/(e^{5x)}	\int\:\frac{8-e^{x}}{e^{5x}}dx
derivative of 3^xtan(ln(x))	derivative\:3^{x}\tan(\ln(x))
integral of x/(x^4)	\int\:\frac{x}{x^{4}}dx
limit as x approaches 0 of (tan(x))/(3x)	\lim\:_{x\to\:0}(\frac{\tan(x)}{3x})
ydy=4x(y^2+1)^{1/2}dx	ydy=4x(y^{2}+1)^{\frac{1}{2}}dx
y^{''}+25y=-40sin(5t)	y^{\prime\:\prime\:}+25y=-40\sin(5t)
(\partial)/(\partial x)(4arctan(xy))	\frac{\partial\:}{\partial\:x}(4\arctan(xy))
integral of 12	\int\:12dx
limit as x approaches 0 of x/(tan(2x))	\lim\:_{x\to\:0}(\frac{x}{\tan(2x)})
derivative of xsqrt(16-x^2)	derivative\:x\sqrt{16-x^{2}}
x(dy)/(dx)-y=x^2y^2	x\frac{dy}{dx}-y=x^{2}y^{2}
integral of 24sin(x)	\int\:24\sin(x)dx
derivative of (2x-1)^2	derivative\:(2x-1)^{2}
integral of 3xe^{3x}	\int\:3xe^{3x}dx
integral from-infinity to 0 of 1/(3-4x)	\int\:_{-\infty\:}^{0}\frac{1}{3-4x}dx
derivative of (200/x)	\frac{d}{dx}(\frac{200}{x})
integral of (15-15x)/(1-sqrt(x))	\int\:\frac{15-15x}{1-\sqrt{x}}dx
integral of y^2sin(8y)	\int\:y^{2}\sin(8y)dy
(sqrt(x)+x)(dy)/(dx)=sqrt(y)+y	(\sqrt{x}+x)\frac{dy}{dx}=\sqrt{y}+y
integral of (23)/(x^3-27)	\int\:\frac{23}{x^{3}-27}dx
derivative of arctan((2x/(1-x^2)))	\frac{d}{dx}(\arctan(\frac{2x}{1-x^{2}}))
integral of arcsin(y)	\int\:\arcsin(y)dy
derivative of ln(5x+1)	\frac{d}{dx}(\ln(5x+1))
derivative of e^{9x}	derivative\:e^{9x}
implicit (dy)/(dx),sqrt(xy)=9+x^2y	implicit\:\frac{dy}{dx},\sqrt{xy}=9+x^{2}y
integral of x(3+2x)^{10}	\int\:x(3+2x)^{10}dx
limit as x approaches 0 of xln(2x)	\lim\:_{x\to\:0}(x\ln(2x))
integral of (2r+1)/(r^2-3r+2)	\int\:\frac{2r+1}{r^{2}-3r+2}dr
limit as x approaches infinity of ((e^{x^5}))/(5-x^6)	\lim\:_{x\to\:\infty\:}(\frac{(e^{x^{5}})}{5-x^{6}})
derivative of sin(cos(3x))	\frac{d}{dx}(\sin(\cos(3x)))
integral of log_{a}(x)	\int\:\log_{a}(x)dx
(dx)/(dt)=tx-2x+t-2	\frac{dx}{dt}=tx-2x+t-2
limit as x approaches 0 of (1-cot(x))/(1/x)	\lim\:_{x\to\:0}(\frac{1-\cot(x)}{\frac{1}{x}})
integral of 6x^5	\int\:6x^{5}dx
derivative of (7x^2/(4e^x-x))	\frac{d}{dx}(\frac{7x^{2}}{4e^{x}-x})
(\partial)/(\partial y)(e^{xyz^3}yz^3)	\frac{\partial\:}{\partial\:y}(e^{xyz^{3}}yz^{3})
integral of 6/(x^2sqrt(x^2-9))	\int\:\frac{6}{x^{2}\sqrt{x^{2}-9}}dx

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