What is the integral of 9/((1-2x)^2) ?

The integral of 9/((1-2x)^2) is 9/(2(1-2x))+C

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integral of 9/((1-2x)^2)

\int \frac{9}{( 1 - 2 x ) ^{2}} d x

\frac{9}{2 ( 1 - 2 x )} + C

Solution steps

\int \frac{9}{( 1 - 2 x ) ^{2}} d x

Take the constant out:

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

= 9 \cdot \int \frac{1}{( 1 - 2 x ) ^{2}} d x

Apply u-substitution

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

= 9 \cdot \int - \frac{1}{2 u ^{2}} d u

Take the constant out:

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

= 9 (- \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

: - \frac{1}{u}

= 9 (- \frac{1}{2} (- \frac{1}{u}))

Substitute back

u = 1 - 2 x

= 9 (- \frac{1}{2} (- \frac{1}{1 - 2 x}))

Simplify

9 (- \frac{1}{2} (- \frac{1}{1 - 2 x})) : \frac{9}{2 ( 1 - 2 x )}

= \frac{9}{2 ( 1 - 2 x )}

Add a constant to the solution

= \frac{9}{2 ( 1 - 2 x )} + C

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What is the integral of 9/((1-2x)^2) ?
The integral of 9/((1-2x)^2) is 9/(2(1-2x))+C