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Popular Calculus Problems

integral of 1/(xsqrt(4x^2-1))	\int\:\frac{1}{x\sqrt{4x^{2}-1}}dx
limit as x approaches 1+of arctan(ln(x-1))	\lim\:_{x\to\:1+}(\arctan(\ln(x-1)))
derivative of sqrt(w)e^{7w}	derivative\:\sqrt{w}e^{7w}
derivative of f(x)=x^{-15}	derivative\:f(x)=x^{-15}
y^'+1/(200+3t)y=12	y^{\prime\:}+\frac{1}{200+3t}y=12
limit as x approaches 0 of ln(1-9x)	\lim\:_{x\to\:0}(\ln(1-9x))
derivative of 1-x^6	\frac{d}{dx}(1-x^{6})
derivative of arctan(2y)	derivative\:\arctan(2y)
(\partial)/(\partial x)(arctan(x-2y))	\frac{\partial\:}{\partial\:x}(\arctan(x-2y))
y^{''}-ay=0	y^{\prime\:\prime\:}-ay=0
derivative of e^x+c	\frac{d}{dx}(e^{x}+c)
derivative of f(x)=sqrt(x^2+x+1)	derivative\:f(x)=\sqrt{x^{2}+x+1}
integral of 1/(p-p^2)	\int\:\frac{1}{p-p^{2}}dp
derivative of arccsc(-x^2)	\frac{d}{dx}(\arccsc(-x^{2}))
integral of (tan^2(x))/(2sec(x))	\int\:\frac{\tan^{2}(x)}{2\sec(x)}dx
integral from 0 to pi of 4xcos(x)	\int\:_{0}^{π}4x\cos(x)dx
derivative of 1/(in(x-1))	\frac{d}{dx}(\frac{1}{in(x-1)})
integral from 0 to 1 of (53)/(x^5)	\int\:_{0}^{1}\frac{53}{x^{5}}dx
(\partial)/(\partial x)(-x/y)	\frac{\partial\:}{\partial\:x}(-\frac{x}{y})
integral from-1 to 1 of (2x-1)^2	\int\:_{-1}^{1}(2x-1)^{2}dx
(dy)/(dx)=-5-5x+y	\frac{dy}{dx}=-5-5x+y
integral of sqrt(2y)	\int\:\sqrt{2y}dy
(\partial)/(\partial x)((x-5)^{1/4}y^{1/4})	\frac{\partial\:}{\partial\:x}((x-5)^{\frac{1}{4}}y^{\frac{1}{4}})
derivative of f(x)=e^xsin(x)	derivative\:f(x)=e^{x}\sin(x)
limit as x approaches 1 of x^2+3	\lim\:_{x\to\:1}(x^{2}+3)
integral of sqrt(x)-1/2 x	\int\:\sqrt{x}-\frac{1}{2}xdx
(\partial)/(\partial y)(tan(2+2x^2y^4z^2))	\frac{\partial\:}{\partial\:y}(\tan(2+2x^{2}y^{4}z^{2}))
derivative of (x^2/(10))	\frac{d}{dx}(\frac{x^{2}}{10})
derivative of f(x)=sqrt(1+2x)	derivative\:f(x)=\sqrt{1+2x}
integral of sqrt((x^3-8)/(x^{11))}	\int\:\sqrt{\frac{x^{3}-8}{x^{11}}}dx
(\partial)/(\partial x)(ln(x^8-y^6))	\frac{\partial\:}{\partial\:x}(\ln(x^{8}-y^{6}))
integral of e^xa^x	\int\:e^{x}a^{x}dx
x^2y^'+y= x/y ,y(1)=4	x^{2}y^{\prime\:}+y=\frac{x}{y},y(1)=4
((y^'-e-t+4))/y =-4	\frac{(y^{\prime\:}-e-t+4)}{y}=-4
limit as x approaches 0 of (7^{sin(x)}-1)/x	\lim\:_{x\to\:0}(\frac{7^{\sin(x)}-1}{x})
integral of 1/9 x^{-8/9}	\int\:\frac{1}{9}x^{-\frac{8}{9}}dx
(\partial)/(\partial x)(x^3e^ysin(x-y))	\frac{\partial\:}{\partial\:x}(x^{3}e^{y}\sin(x-y))
tangent of f(x)=x^2-3,(3,6)	tangent\:f(x)=x^{2}-3,(3,6)
maclaurin (4x)/(x^2+2x-3)	maclaurin\:\frac{4x}{x^{2}+2x-3}
derivative of 1/(5-11e^x)	\frac{d}{dx}(\frac{1}{5-11e^{x}})
integral of 2/3 x^{1/2}	\int\:\frac{2}{3}x^{\frac{1}{2}}dx
integral of (x^3)/(e^{x^2)}	\int\:\frac{x^{3}}{e^{x^{2}}}dx
limit as x approaches 0 of 1/(3+2^{1/x)}	\lim\:_{x\to\:0}(\frac{1}{3+2^{\frac{1}{x}}})
(x^2+1)y^'+3xy=6x	(x^{2}+1)y^{\prime\:}+3xy=6x
integral of sin^3(3x)cos^6(3x)	\int\:\sin^{3}(3x)\cos^{6}(3x)dx
integral of xln(sqrt(5x))	\int\:x\ln(\sqrt{5x})dx
integral of 2x+y^2	\int\:2x+y^{2}dx
area y=10-(x+2)^2,(-5.2,1.2)	area\:y=10-(x+2)^{2},(-5.2,1.2)
integral of x+e^{5x}	\int\:x+e^{5x}dx
9y^{''}+6y^'+4y=0	9y^{\prime\:\prime\:}+6y^{\prime\:}+4y=0
integral of 2e^t	\int\:2e^{t}dt
(dy)/(dx)= x/y ,y(0)=-5	\frac{dy}{dx}=\frac{x}{y},y(0)=-5
derivative of ln(1/(2x))	\frac{d}{dx}(\ln(\frac{1}{2x}))
derivative of y=3e^xcos(x)	derivative\:y=3e^{x}\cos(x)
integral of (x/7-3/4 x^4)	\int\:(\frac{x}{7}-\frac{3}{4}x^{4})dx
2t^2y^{''}+3ty^'-y=0	2t^{2}y^{\prime\:\prime\:}+3ty^{\prime\:}-y=0
integral from 0 to infinity of e^{-x/2}	\int\:_{0}^{\infty\:}e^{-\frac{x}{2}}dx
limit as x approaches 3 of 1/(3-x)	\lim\:_{x\to\:3}(\frac{1}{3-x})
y^'=(4x^4e^{y/x}+x^2y^2)/(x^3y)	y^{\prime\:}=\frac{4x^{4}e^{\frac{y}{x}}+x^{2}y^{2}}{x^{3}y}
integral of x^3sqrt(x^2-81)	\int\:x^{3}\sqrt{x^{2}-81}dx
d/(dy)((y/8)^4+1/(4y^2))	\frac{d}{dy}((\frac{y}{8})^{4}+\frac{1}{4y^{2}})
x^2y^{''}-2y=0	x^{2}y^{\prime\:\prime\:}-2y=0
limit as x approaches 1 of cos(pi)x	\lim\:_{x\to\:1}(\cos(π)x)
sum from n=1 to infinity of 4(2/3)^{n-1}	\sum\:_{n=1}^{\infty\:}4(\frac{2}{3})^{n-1}
integral of 1/(x^3+x)	\int\:\frac{1}{x^{3}+x}dx
derivative of 2^{x^2+3x}	\frac{d}{dx}(2^{x^{2}+3x})
integral of (x+5)cos(x)	\int\:(x+5)\cos(x)dx
integral of xcos^2(9x)	\int\:x\cos^{2}(9x)dx
(dy)/(dx)=4xe^y	\frac{dy}{dx}=4xe^{y}
derivative of (x^3+1(3-2x^3))	\frac{d}{dx}((x^{3}+1)(3-2x^{3}))
slope of (3,2),(5,6)	slope\:(3,2),(5,6)
derivative of (x-5xsqrt(x)/(sqrt(x)))	\frac{d}{dx}(\frac{x-5x\sqrt{x}}{\sqrt{x}})
tangent of f(x)=5x-4x^2,\at x=-1	tangent\:f(x)=5x-4x^{2},\at\:x=-1
integral from 0 to 3 of (2^x)	\int\:_{0}^{3}(2^{x})dx
limit as x approaches 3-of 1/(6-2x)	\lim\:_{x\to\:3-}(\frac{1}{6-2x})
inverse oflaplace 1/(s^2-2s+5)	inverselaplace\:\frac{1}{s^{2}-2s+5}
derivative of (8+xf(x))/(sqrt(x))	derivative\:\frac{8+xf(x)}{\sqrt{x}}
tangent of x^2-2x+1	tangent\:x^{2}-2x+1
limit as x approaches 0+of 5/(x^2)	\lim\:_{x\to\:0+}(\frac{5}{x^{2}})
(x+y)^2dx+(2xy+x^2-8)dy=0	(x+y)^{2}dx+(2xy+x^{2}-8)dy=0
limit as x approaches 0 of (3x+1)/(7x)	\lim\:_{x\to\:0}(\frac{3x+1}{7x})
integral of (x-1)^2x^3(2-x)	\int\:(x-1)^{2}\cdot\:x^{3}\cdot\:(2-x)dx
(dy)/(dx)=(5x)/(9y)	\frac{dy}{dx}=\frac{5x}{9y}
derivative of 7e^e	\frac{d}{dx}(7e^{e})
(\partial)/(\partial x)((x^3+y^2)^{1/2})	\frac{\partial\:}{\partial\:x}((x^{3}+y^{2})^{\frac{1}{2}})
limit as x approaches-infinity of x/(9-x^2)	\lim\:_{x\to\:-\infty\:}(\frac{x}{9-x^{2}})
integral from 0 to 2 of (x+1)/(x(x^2+1))	\int\:_{0}^{2}\frac{x+1}{x(x^{2}+1)}dx
sum from n=1 to infinity of 1/(n*3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n\cdot\:3^{n}}
limit as x approaches-infinity of 3-x	\lim\:_{x\to\:-\infty\:}(3-x)
inverse oflaplace 4/(2s^2+2s+1)	inverselaplace\:\frac{4}{2s^{2}+2s+1}
derivative of y=e^4x^2+1	derivative\:y=e^{4}x^{2}+1
(\partial)/(\partial y)(3x^2y^2+1)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{2}+1)
x/((1+x^2))dx+y/((1+y^2))dy=0	\frac{x}{(1+x^{2})}dx+\frac{y}{(1+y^{2})}dy=0
f(x)=(2x)/(1+x^2)	f(x)=\frac{2x}{1+x^{2}}
63x^2y^{''}+14x(x-9)y^'-14(x-9)y=-2x^3	63x^{2}y^{\prime\:\prime\:}+14x(x-9)y^{\prime\:}-14(x-9)y=-2x^{3}
tangent of y=x^2-x	tangent\:y=x^{2}-x
derivative of 2^{10x}	\frac{d}{dx}(2^{10x})
integral of x^3sqrt(256-x^2)	\int\:x^{3}\sqrt{256-x^{2}}dx
derivative of cos(x/3 sin(x))	\frac{d}{dx}(\cos(\frac{x}{3})\sin(x))
d/(dt)(1/(2sqrt(t)))	\frac{d}{dt}(\frac{1}{2\sqrt{t}})

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