What is the integral of (x^2)/((10-x)(10+x)) ?

The integral of (x^2)/((10-x)(10+x)) is -x+10(1/2 ln| x/(10)+1|-1/2 ln| x/(10)-1|)+C

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integral of (x^2)/((10-x)(10+x))

\int \frac{x ^{2}}{( 10 - x ) ( 10 + x )} d x

- x + 10 (\frac{1}{2} ln \frac{x}{10} + 1 - \frac{1}{2} ln \frac{x}{10} - 1) + C

Solution steps

\int \frac{x ^{2}}{( 10 - x ) ( 10 + x )} d x

Long division

\frac{x ^{2}}{( 10 - x ) ( 10 + x )} : - 1 + \frac{100}{- x ^{2} + 100}

= \int - 1 + \frac{100}{- x ^{2} + 100} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1 d x + \int \frac{100}{- x ^{2} + 100} d x

\int 1 d x = x

\int \frac{100}{- x ^{2} + 100} d x = 10 (\frac{1}{2} ln \frac{x}{10} + 1 - \frac{1}{2} ln \frac{x}{10} - 1)

= - x + 10 (\frac{1}{2} ln \frac{x}{10} + 1 - \frac{1}{2} ln \frac{x}{10} - 1)

Add a constant to the solution

= - x + 10 (\frac{1}{2} ln \frac{x}{10} + 1 - \frac{1}{2} ln \frac{x}{10} - 1) + C

\int sin^{3} (x co) s^{10} x d x

\frac{d}{d x} (\frac{1}{a + b x + c x ^{2}} + 0.003)

\frac{\partial}{\partial y} (cos (2 x) y)

\frac{d y}{d x} = \frac{x - 1}{y + 2}

x \to 3 lim (x^{2} - 2)

What is the integral of (x^2)/((10-x)(10+x)) ?
The integral of (x^2)/((10-x)(10+x)) is -x+10(1/2 ln| x/(10)+1|-1/2 ln| x/(10)-1|)+C