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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \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

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

Apply the Power Rule

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

Substitute back

u = 1 - 2 x

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

Simplify

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

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

Add a constant to the solution

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

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