What is the integral from 0 to x of 1/((1-x)^{2.5)} ?

The integral from 0 to x of 1/((1-x)^{2.5)} is (0.66666…)/((1-x)^{1.5)}-0.66666…

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integral from 0 to x of 1/((1-x)^{2.5)}

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.5}} d x

\frac{0.66666 \dots}{( 1 - x ) ^{1.5}} - 0.66666 \dots

Solution steps

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.5}} d x

Apply u-substitution

= \int_{1}^{1 - x} - \frac{1}{u ^{2.5}} 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 ^{2.5}} d u

Apply the Power Rule

= - [- \frac{0.66666 \dots}{u ^{1.5}}]_{1}^{1 - x}

Compute the boundaries:

- \frac{0.66666 \dots}{( 1 - x ) ^{1.5}} + 0.66666 \dots

= - (- \frac{0.66666 \dots}{( 1 - x ) ^{1.5}} + 0.66666 \dots)

Simplify

= \frac{0.66666 \dots}{( 1 - x ) ^{1.5}} - 0.66666 \dots

What is the integral from 0 to x of 1/((1-x)^{2.5)} ?
The integral from 0 to x of 1/((1-x)^{2.5)} is (0.66666…)/((1-x)^{1.5)}-0.66666…