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Popular Calculus Problems

integral of x/(4+5x^2)	\int\:\frac{x}{4+5x^{2}}dx
integral of (4/x+9/(x^7))	\int\:(\frac{4}{x}+\frac{9}{x^{7}})dx
integral of 1/((sin(x)+tan(x)))	\int\:\frac{1}{(\sin(x)+\tan(x))}dx
(\partial)/(\partial x)(sqrt(1-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{1-y^{2}})
integral of 1/(sqrt(-x^2-4x))	\int\:\frac{1}{\sqrt{-x^{2}-4x}}dx
limit as h approaches 0 of ((1+h)^8-1)/h	\lim\:_{h\to\:0}(\frac{(1+h)^{8}-1}{h})
integral of ln(2x+3)	\int\:\ln(2x+3)dx
integral of (5-x^2)/((x^2+9)(3-x))	\int\:\frac{5-x^{2}}{(x^{2}+9)(3-x)}dx
inverse oflaplace 2/((s+1)(s+2)^2)	inverselaplace\:\frac{2}{(s+1)(s+2)^{2}}
(dy)/(dx)=-(e^xy^2)/(10)	\frac{dy}{dx}=-\frac{e^{x}y^{2}}{10}
integral of 3ln^2(x)	\int\:3\ln^{2}(x)dx
(dy)/(dt)(t)-2y=3e^t	\frac{dy}{dt}(t)-2y=3e^{t}
integral of (4x+2)/((x+1)(x^2+1))	\int\:\frac{4x+2}{(x+1)(x^{2}+1)}dx
derivative of 1000(1-x/(500)^2)	\frac{d}{dx}(1000(1-\frac{x}{500})^{2})
(dy)/(dx)=4+9x+32y+72xy	\frac{dy}{dx}=4+9x+32y+72xy
integral from 0 to t of e^ssin(t-s)	\int\:_{0}^{t}e^{s}\sin(t-s)ds
derivative of f(s)=-(12)/(s^5)	derivative\:f(s)=-\frac{12}{s^{5}}
derivative of xln(x^{15})	\frac{d}{dx}(x\ln(x^{15}))
derivative of 1/27 (9x^2+6)^{3/2}	derivative\:\frac{1}{27}(9x^{2}+6)^{\frac{3}{2}}
limit as x approaches infinity of x/3	\lim\:_{x\to\:\infty\:}(\frac{x}{3})
integral of 1/(sqrt(e^x+1))	\int\:\frac{1}{\sqrt{e^{x}+1}}dx
sum from n=0 to infinity of 1/((2n+1)^3)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n+1)^{3}}
limit as n approaches infinity of-7^n	\lim\:_{n\to\:\infty\:}(-7^{n})
inverse oflaplace 1/(s(s^2+100))	inverselaplace\:\frac{1}{s(s^{2}+100)}
(\partial)/(\partial x)(xye^{7y})	\frac{\partial\:}{\partial\:x}(xye^{7y})
derivative of y=ln(x^3+1)	derivative\:y=\ln(x^{3}+1)
sum from n=0 to infinity of 1/3	\sum\:_{n=0}^{\infty\:}\frac{1}{3}
integral from 0 to 1 of (8x^2-2)e^x	\int\:_{0}^{1}(8x^{2}-2)e^{x}dx
d/(dt)((arccos(t))^2)	\frac{d}{dt}((\arccos(t))^{2})
integral of 2cos^3(4x)	\int\:2\cos^{3}(4x)dx
(\partial)/(\partial v)(2uv)	\frac{\partial\:}{\partial\:v}(2uv)
derivative of (f(x))/(x^7)	derivative\:\frac{f(x)}{x^{7}}
limit as x approaches 0 of (5+x)^x	\lim\:_{x\to\:0}((5+x)^{x})
(2xe^x-y^2)dx+2ydy=0	(2xe^{x}-y^{2})dx+2ydy=0
derivative of y=(x^4+2)^2(x^3+4)^4	derivative\:y=(x^{4}+2)^{2}(x^{3}+4)^{4}
integral of-3x^2sin(pix)	\int\:-3x^{2}\sin(πx)dx
y^{''}-2y^'-15y=3	y^{\prime\:\prime\:}-2y^{\prime\:}-15y=3
(\partial)/(\partial x)(x^{1/2}*y)	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}\cdot\:y)
derivative of (x-2/x ^4)	\frac{d}{dx}((x-\frac{2}{x})^{4})
tangent of f(x)=2x^2,\at x=0	tangent\:f(x)=2x^{2},\at\:x=0
integral of 4x^{-3}	\int\:4x^{-3}dx
integral of 1/((x+1)(x-1))	\int\:\frac{1}{(x+1)(x-1)}dx
derivative of f(x)=(2x-4)(2x^3-x^2+1)	derivative\:f(x)=(2x-4)(2x^{3}-x^{2}+1)
tangent of y= 1/((1+x^2))	tangent\:y=\frac{1}{(1+x^{2})}
limit as h(y,w) approaches 0 of (y-h(y,w))^{w(y)}	\lim\:_{h(y,w)\to\:0}((y-h(y,w))^{w(y)})
limit as x approaches 0 of ((x^2))/(\|x\|)	\lim\:_{x\to\:0}(\frac{(x^{2})}{\left\|x\right\|})
(dy)/(dx)-y=8	\frac{dy}{dx}-y=8
slope of (0,2),(5,-2)	slope\:(0,2),(5,-2)
integral from 0 to 1 of sin^4(1/2 pix)	\int\:_{0}^{1}\sin^{4}(\frac{1}{2}πx)dx
inverse oflaplace-(0.625)/(s+4)	inverselaplace\:-\frac{0.625}{s+4}
(\partial)/(\partial x)((5x-6y)/(5x+6y))	\frac{\partial\:}{\partial\:x}(\frac{5x-6y}{5x+6y})
integral from 0 to 5/2 of c(2x-x^2)	\int\:_{0}^{\frac{5}{2}}c(2x-x^{2})dx
integral of 9x^{13}e^{-x^7}	\int\:9x^{13}e^{-x^{7}}dx
integral of 1+1/(x-1)	\int\:1+\frac{1}{x-1}dx
integral of 1/(x^2+4x+29)	\int\:\frac{1}{x^{2}+4x+29}dx
taylor x^{1/3}	taylor\:x^{\frac{1}{3}}
derivative of-e^x(x+6)	\frac{d}{dx}(-e^{x}(x+6))
limit as x approaches 3+of (4-x)/(9-x^2)	\lim\:_{x\to\:3+}(\frac{4-x}{9-x^{2}})
integral of (sin(3x))/(3+3cos(3x))	\int\:\frac{\sin(3x)}{3+3\cos(3x)}dx
implicit (dy)/(dx),3xy=6	implicit\:\frac{dy}{dx},3xy=6
integral from-1 to 2 of (x^3)	\int\:_{-1}^{2}(x^{3})dx
area f(x)=2x+1,1,5	area\:f(x)=2x+1,1,5
f(x)=\sqrt[3]{x^2}+sqrt(x)	f(x)=\sqrt[3]{x^{2}}+\sqrt{x}
integral of sin(pi)	\int\:\sin(π)
limit as x approaches infinity of y/x	\lim\:_{x\to\:\infty\:}(\frac{y}{x})
limit as x approaches+0 of 5x^2	\lim\:_{x\to\:+0}(5x^{2})
d/(dt)(-2)	\frac{d}{dt}(-2)
x^'=sin(x)	x^{\prime\:}=\sin(x)
limit as x approaches 3 of \|x-3\|	\lim\:_{x\to\:3}(\left\|x-3\right\|)
(\partial)/(\partial x)(2x^{7y})	\frac{\partial\:}{\partial\:x}(2x^{7y})
(\partial)/(\partial x)(2y+x+1)	\frac{\partial\:}{\partial\:x}(2y+x+1)
f(X)=sqrt(X)	f(X)=\sqrt{X}
integral of (xe^{2x})/((2x+1)^2)	\int\:\frac{xe^{2x}}{(2x+1)^{2}}dx
x(dy)/(dx)+2y=x^{-4}	x\frac{dy}{dx}+2y=x^{-4}
f(t)=sqrt(2t+1)	f(t)=\sqrt{2t+1}
inverse oflaplace s/((s^2+2^2)^2)	inverselaplace\:\frac{s}{(s^{2}+2^{2})^{2}}
(\partial)/(\partial x)(e^{xcos(y)}sin(xy))	\frac{\partial\:}{\partial\:x}(e^{x\cos(y)}\sin(xy))
derivative of (x^2-4)^2	derivative\:(x^{2}-4)^{2}
integral of (9x^3-x^2+45x+5)/(x^3+5x)	\int\:\frac{9x^{3}-x^{2}+45x+5}{x^{3}+5x}dx
limit as x approaches 2 of x^4-16	\lim\:_{x\to\:2}(x^{4}-16)
integral of 5te^t	\int\:5te^{t}dt
limit as x approaches 6-of (x+1)/(x-6)	\lim\:_{x\to\:6-}(\frac{x+1}{x-6})
derivative of (4x^2-3/(x+4))	\frac{d}{dx}(\frac{4x^{2}-3}{x+4})
derivative of (2x+8^2)	\frac{d}{dx}((2x+8)^{2})
limit as x approaches 0 of (sin(5)(x))/x	\lim\:_{x\to\:0}(\frac{\sin(5)(x)}{x})
integral of (3x)/((3x^2+2)^3)	\int\:\frac{3x}{(3x^{2}+2)^{3}}dx
derivative of arccos(1)(4x^2)	derivative\:\arccos(1)(4x^{2})
integral from 0 to N of e^{-st}cos(2t)	\int\:_{0}^{N}e^{-st}\cos(2t)dt
integral of (16x^3)/(sqrt(1-16x^8))	\int\:\frac{16x^{3}}{\sqrt{1-16x^{8}}}dx
limit as x approaches-6 of 1/((x+6)^4)	\lim\:_{x\to\:-6}(\frac{1}{(x+6)^{4}})
y^{''}-5y^'+4y=5sin(5t)	y^{\prime\:\prime\:}-5y^{\prime\:}+4y=5\sin(5t)
integral from 1 to e^x of ln(t)	\int\:_{1}^{e^{x}}\ln(t)dt
integral of F(x)	\int\:F(x)dx
d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}+ln({x}{y}{z}))	\frac{d}{d{y}}(({x}^{2}+{y}^{2}+{z}^{2})^{-\frac{1}{2}}+\ln({x}{y}{z}))
integral of tan^7(x)sec^4(x)	\int\:\tan^{7}(x)\sec^{4}(x)dx
limit as x approaches-2 of 5(3x^2-24x+3)	\lim\:_{x\to\:-2}(5(3x^{2}-24x+3))
limit as x approaches 0 of (-9)/(1-9x)	\lim\:_{x\to\:0}(\frac{-9}{1-9x})
(\partial)/(\partial x)(y*cos(x))	\frac{\partial\:}{\partial\:x}(y\cdot\:\cos(x))
integral of (11x^{10}-(10)/(x^{10)})	\int\:(11x^{10}-\frac{10}{x^{10}})dx
derivative of 3x^2+5x-1	\frac{d}{dx}(3x^{2}+5x-1)

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