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Popular Calculus Problems

sum from n=3 to infinity of 2/(nln^2(n))	\sum\:_{n=3}^{\infty\:}\frac{2}{n\ln^{2}(n)}
area y=x,y=3sqrt(x)	area\:y=x,y=3\sqrt{x}
integral of x/((5x^2+2)^6)	\int\:\frac{x}{(5x^{2}+2)^{6}}dx
integral from 0 to 1 of 1/(1+x)	\int\:_{0}^{1}\frac{1}{1+x}dx
y^{''}+4y^'+5y=5x-1	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=5x-1
(\partial ^2)/(\partial x\partial y)(y^4cos(2x))	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(y^{4}\cos(2x))
(\partial)/(\partial y)(sqrt(16-x^2-4y))	\frac{\partial\:}{\partial\:y}(\sqrt{16-x^{2}-4y})
y^{''}-y=sin(2t)	y^{\prime\:\prime\:}-y=\sin(2t)
derivative of f(x)=(e^x)/(x+3)	derivative\:f(x)=\frac{e^{x}}{x+3}
inverse oflaplace ((s+5))/((s^2+4s+13))	inverselaplace\:\frac{(s+5)}{(s^{2}+4s+13)}
derivative of x^2(1-x^3)	\frac{d}{dx}(x^{2}(1-x)^{3})
integral of ((tan^3(ln(x))))/(6x)	\int\:\frac{(\tan^{3}(\ln(x)))}{6x}dx
9y^{''}+10y=0	9y^{\prime\:\prime\:}+10y=0
(\partial)/(\partial v)(u)	\frac{\partial\:}{\partial\:v}(u)
integral from 1 to 2 of (x^2+1/(4x^2))	\int\:_{1}^{2}(x^{2}+\frac{1}{4x^{2}})dx
integral of y/(sqrt(2x+3y))	\int\:\frac{y}{\sqrt{2x+3y}}dx
derivative of x^2e^xcos(2x)	\frac{d}{dx}(x^{2}e^{x}\cos(2x))
derivative of-6cot(xcsc(x))	\frac{d}{dx}(-6\cot(x)\csc(x))
(\partial)/(\partial x)((1+2x^2)(x-x^2))	\frac{\partial\:}{\partial\:x}((1+2x^{2})(x-x^{2}))
slope ofintercept (7.2)(2.8)	slopeintercept\:(7.2)(2.8)
integral from-6 to 6 of sqrt(58)	\int\:_{-6}^{6}\sqrt{58}
limit as x approaches 4 of (\|x\|)/x	\lim\:_{x\to\:4}(\frac{\left\|x\right\|}{x})
derivative of 1/(sqrt(2+x^2))	\frac{d}{dx}(\frac{1}{\sqrt{2+x^{2}}})
tangent of (x^2)/(4+sqrt(x))	tangent\:\frac{x^{2}}{4+\sqrt{x}}
sum from n=0 to infinity of 1/(3n+2)	\sum\:_{n=0}^{\infty\:}\frac{1}{3n+2}
sum from n=4 to infinity of 2/(n^2-1)	\sum\:_{n=4}^{\infty\:}\frac{2}{n^{2}-1}
limit as n approaches infinity of-2(n-4)	\lim\:_{n\to\:\infty\:}(-2(n-4))
sum from n=3 to infinity of (4^n)/(5^n)	\sum\:_{n=3}^{\infty\:}\frac{4^{n}}{5^{n}}
derivative of ab^x	\frac{d}{dx}(ab^{x})
derivative of x^3(x-1)^2	derivative\:x^{3}(x-1)^{2}
integral of (x+1)/((x-1)^3)	\int\:\frac{x+1}{(x-1)^{3}}dx
integral of (tan(x))/1	\int\:\frac{\tan(x)}{1}dx
y^'=t-2y	y^{\prime\:}=t-2y
integral from 2 to infinity of 1/(x^4)	\int\:_{2}^{\infty\:}\frac{1}{x^{4}}dx
tangent of f(x)=x^2-7x+12,\at x=2	tangent\:f(x)=x^{2}-7x+12,\at\:x=2
derivative of y=sqrt(4-\sqrt{4+x)}	derivative\:y=\sqrt{4-\sqrt{4+x}}
d/(dr(t))((s-r(t))/t)	\frac{d}{dr(t)}(\frac{s-r(t)}{t})
(\partial)/(\partial x)(e-4tcos(pix))	\frac{\partial\:}{\partial\:x}(e-4t\cos(πx))
integral of-cos(x)sin^2(x)	\int\:-\cos(x)\sin^{2}(x)dx
sum from n=2 to infinity of 5/(4^n)	\sum\:_{n=2}^{\infty\:}\frac{5}{4^{n}}
integral from 2 to 4 of 1/(sqrt(4x-x^2))	\int\:_{2}^{4}\frac{1}{\sqrt{4x-x^{2}}}dx
(\partial)/(\partial x)(xe^{9xy})	\frac{\partial\:}{\partial\:x}(xe^{9xy})
integral from 4 to 10 of 6	\int\:_{4}^{10}6dx
integral of ke^{-k^2}	\int\:ke^{-k^{2}}
derivative of 10+((50x/(2x^2+9)))	\frac{d}{dx}(10+(\frac{50x}{2x^{2}+9}))
limit as x approaches 0-of 6/x-6/(\|x\|)	\lim\:_{x\to\:0-}(\frac{6}{x}-\frac{6}{\left\|x\right\|})
xy^'+y=x^4y^3	x\cdot\:y^{\prime\:}+y=x^{4}\cdot\:y^{3}
integral of t^{19}e^{-t^{20}}	\int\:t^{19}e^{-t^{20}}dt
inverse oflaplace 5/(s^3-2s^2-3s)	inverselaplace\:\frac{5}{s^{3}-2s^{2}-3s}
slope ofintercept (2005,56),(2010,59)	slopeintercept\:(2005,56),(2010,59)
integral from 0 to 1 of 3/(x^2-x-2)	\int\:_{0}^{1}\frac{3}{x^{2}-x-2}dx
derivative of 3/(x^2)	derivative\:\frac{3}{x^{2}}
sum from n=1 to infinity of (-1)^ne^{-n}	\sum\:_{n=1}^{\infty\:}(-1)^{n}e^{-n}
limit as x approaches 2 of 3x-9	\lim\:_{x\to\:2}(3x-9)
derivative of-125cos(5x)	\frac{d}{dx}(-125\cos(5x))
integral from 1/2 to 3/4 of 1/(u^2)	\int\:_{\frac{1}{2}}^{\frac{3}{4}}\frac{1}{u^{2}}du
integral from-1 to 3 of 3x^2+4x	\int\:_{-1}^{3}3x^{2}+4xdx
derivative of y=arcsec(x^2+1)	derivative\:y=\arcsec(x^{2}+1)
parity y=ln(x^3-2x^2+2)	parity\:y=\ln(x^{3}-2x^{2}+2)
limit as x approaches infinity of 2/x+1	\lim\:_{x\to\:\infty\:}(\frac{2}{x}+1)
integral of 10sin(t)+3cos(t)	\int\:10\sin(t)+3\cos(t)dt
(\partial)/(\partial x)(xsqrt(y))	\frac{\partial\:}{\partial\:x}(x\sqrt{y})
derivative of (e^x/(1+x))	\frac{d}{dx}(\frac{e^{x}}{1+x})
tangent of y=7cos(x),(pi/3 ,3.5)	tangent\:y=7\cos(x),(\frac{π}{3},3.5)
inverse oflaplace 2/(s^2+2s)	inverselaplace\:\frac{2}{s^{2}+2s}
(dy)/(dt)= 9/40-y/(200),y(0)=90	\frac{dy}{dt}=\frac{9}{40}-\frac{y}{200},y(0)=90
integral of (4\sqrt[3]{x}-2xsqrt(x))	\int\:(4\sqrt[3]{x}-2x\sqrt{x})dx
d/(dt)(7cos(t))	\frac{d}{dt}(7\cos(t))
derivative of y=ln(1+sin(sqrt(x)))	derivative\:y=\ln(1+\sin(\sqrt{x}))
integral of (sin(x))/(7+cos^2(x))	\int\:\frac{\sin(x)}{7+\cos^{2}(x)}dx
derivative of 4x^4-32x^3+89x^2-95x+29	\frac{d}{dx}(4x^{4}-32x^{3}+89x^{2}-95x+29)
limit as x approaches-5+of (x+4)/(x+5)	\lim\:_{x\to\:-5+}(\frac{x+4}{x+5})
integral from 0 to 2 of 4x-2x^2	\int\:_{0}^{2}4x-2x^{2}dx
laplacetransform t+sin(t)	laplacetransform\:t+\sin(t)
laplacetransform sin(2t)cos(5t)	laplacetransform\:\sin(2t)\cos(5t)
integral of (-3x^2)/(sqrt(1-x))	\int\:\frac{-3x^{2}}{\sqrt{1-x}}dx
integral of 8ln(x^2-1)	\int\:8\ln(x^{2}-1)dx
(\partial)/(\partial y)(zarctan(y/x))	\frac{\partial\:}{\partial\:y}(z\arctan(\frac{y}{x}))
f(x)= 1/(xln(x))	f(x)=\frac{1}{x\ln(x)}
integral from 0 to 1 of sqrt(64t^2+9t^4)	\int\:_{0}^{1}\sqrt{64t^{2}+9t^{4}}dt
derivative of tan(sqrt(3t))	derivative\:\tan(\sqrt{3t})
integral of ln(7x+5)	\int\:\ln(7x+5)dx
integral of 2tsqrt(2t-3)	\int\:2t\sqrt{2t-3}dt
x^'(t)=(1/3 x)(1-x/3),x(0)=6	x^{\prime\:}(t)=(\frac{1}{3}x)(1-\frac{x}{3}),x(0)=6
integral from 1 to 2 of 21x^24^{x^3}	\int\:_{1}^{2}21x^{2}4^{x^{3}}dx
integral of 2x^2y+4	\int\:2x^{2}y+4dy
derivative of 4x^2+2	\frac{d}{dx}(4x^{2}+2)
integral from 0 to 16 of 2sqrt(x)-x/2	\int\:_{0}^{16}2\sqrt{x}-\frac{x}{2}dx
limit as x approaches-1 of \|x\|	\lim\:_{x\to\:-1}(\left\|x\right\|)
y^{''}-4y^'+13y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+13y=0
area f(x)= 2/(x^2+1),\|x\|	area\:f(x)=\frac{2}{x^{2}+1},\left\|x\right\|
integral of (x-1)^2sin^2(x)	\int\:(x-1)^{2}\sin^{2}(x)dx
tangent of f(x)= 9/(x^2),\at x=3	tangent\:f(x)=\frac{9}{x^{2}},\at\:x=3
(\partial)/(\partial x)(e^{-7y}sin(7x))	\frac{\partial\:}{\partial\:x}(e^{-7y}\sin(7x))
derivative of (4x/(5sqrt(2))+3)	\frac{d}{dx}(\frac{4x}{5\sqrt{2}}+3)
laplacetransform 25t^2	laplacetransform\:25t^{2}
derivative of f(t)=7-1/3 t	derivative\:f(t)=7-\frac{1}{3}t
integral of (7x^2+5x+7)/((x^2+1)^2)	\int\:\frac{7x^{2}+5x+7}{(x^{2}+1)^{2}}dx
(\partial)/(\partial y)(y^3)	\frac{\partial\:}{\partial\:y}(y^{3})
integral of sin(x)cos^{-4}(x)	\int\:\sin(x)\cos^{-4}(x)dx

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