What is the integral of (4s)/((1-2s^2)^2) ?

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

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integral of (4s)/((1-2s^2)^2)

\int \frac{4 s}{( 1 - 2 s ^{2} ) ^{2}} d s

\frac{1}{1 - 2 s ^{2}} + C

Solution steps

\int \frac{4 s}{( 1 - 2 s ^{2} ) ^{2}} d s

Take the constant out:

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

= 4 \cdot \int \frac{s}{( 1 - 2 s ^{2} ) ^{2}} d s

Apply u-substitution

= 4 \cdot \int - \frac{1}{4 u ^{2}} d u

Take the constant out:

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

= 4 (- \frac{1}{4} \cdot \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

= 4 (- \frac{1}{4} (- \frac{1}{u}))

Substitute back

u = 1 - 2 s^{2}

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

Simplify

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

= \frac{1}{1 - 2 s ^{2}}

Add a constant to the solution

= \frac{1}{1 - 2 s ^{2}} + C

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