What is the integral of 1/((1-x)^{1.5)} ?

The integral of 1/((1-x)^{1.5)} is 2/(sqrt(1-x))+C

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integral of 1/((1-x)^{1.5)}

\int \frac{1}{( 1 - x ) ^{1.5}} d x

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

Solution steps

\int \frac{1}{( 1 - x ) ^{1.5}} d x

Apply u-substitution

: \int - \frac{1}{u ^{1.5}} d u

= \int - \frac{1}{u ^{1.5}} d u

Take the constant out:

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

= - \int \frac{1}{u ^{1.5}} d u

Apply the Power Rule

: - \frac{2}{u}

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

Substitute back

u = 1 - x

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

Simplify

= \frac{2}{1 - x}

Add a constant to the solution

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

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What is the integral of 1/((1-x)^{1.5)} ?
The integral of 1/((1-x)^{1.5)} is 2/(sqrt(1-x))+C