What is the integral of x/((1-x^2)^3) ?

The integral of x/((1-x^2)^3) is 1/(4(1-x^2)^2)+C

Popular >

integral of x/((1-x^2)^3)

\int \frac{x}{( 1 - x ^{2} ) ^{3}} d x

\frac{1}{4 ( 1 - x ^{2} ) ^{2}} + C

Solution steps

\int \frac{x}{( 1 - x ^{2} ) ^{3}} d x

Apply u-substitution

: \int - \frac{1}{2 u ^{3}} d u

= \int - \frac{1}{2 u ^{3}} 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 ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2} (- \frac{1}{2 u ^{2}})

Substitute back

u = 1 - x^{2}

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

Simplify

- \frac{1}{2} (- \frac{1}{2 ( 1 - x ^{2} ) ^{2}}) : \frac{1}{4 ( 1 - x ^{2} ) ^{2}}

= \frac{1}{4 ( 1 - x ^{2} ) ^{2}}

Add a constant to the solution

= \frac{1}{4 ( 1 - x ^{2} ) ^{2}} + C

x^{\frac{2}{3}}, 1

y = (x^{3} + 1) (3 x^{2} - 4 x + 2), (1, 2)

(\frac{1}{y ^{2}} - \frac{8}{y ^{4}}) (y + 2 y^{3})

\frac{5}{s ^{2} + 1}

\frac{d}{d x} ((x + \frac{1}{x ^{3}})^{2})

What is the integral of x/((1-x^2)^3) ?
The integral of x/((1-x^2)^3) is 1/(4(1-x^2)^2)+C