What is the integral of x/((1-x^2)) ?

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

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integral of x/((1-x^2))

integral

\frac{x}{( 1 - x ^{2} )}

- \frac{1}{2} ln 1 - x^{2} + C

Solution steps

\int \frac{x}{1 - x ^{2}} d x

Apply u-substitution

= \int - \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{2} ln ∣ u ∣

Substitute back

u = 1 - x^{2}

= - \frac{1}{2} ln 1 - x^{2}

Add a constant to the solution

= - \frac{1}{2} ln 1 - x^{2} + C

in t e g r a l \frac{e ^{x}}{x ^{2}}

in t e g r a l \frac{x}{81 x ^{4} - 1}

in t e g r a l \frac{1}{( 4 - x ^{2} )}

in t e g r a l \frac{1}{( x ^{2} + x + 1 )}

in t e g r a l cos^{3} (x) - cos (x)

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