What is the integral from 0 to x of 1/((1-x)^{1.5)} ?

The integral from 0 to x of 1/((1-x)^{1.5)} is 2/(sqrt(1-x))-2

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integral from 0 to x of 1/((1-x)^{1.5)}

\int_{0}^{x} \frac{1}{( 1 - x ) ^{1.5}} d x

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

Solution steps

\int_{0}^{x} \frac{1}{( 1 - x ) ^{1.5}} d x

Apply u-substitution

: \int_{1}^{1 - x} - \frac{1}{u ^{1.5}} d u

= \int_{1}^{1 - x} - \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_{1}^{1 - x} \frac{1}{u ^{1.5}} d u

Apply the Power Rule

: [- \frac{2}{u}]_{1}^{1 - x}

= - [- \frac{2}{u}]_{1}^{1 - x}

Compute the boundaries:

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

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

Simplify

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

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What is the integral from 0 to x of 1/((1-x)^{1.5)} ?
The integral from 0 to x of 1/((1-x)^{1.5)} is 2/(sqrt(1-x))-2