What is the integral from 0 to x of 1/((1-x)^{0.4)} ?

The integral from 0 to x of 1/((1-x)^{0.4)} is -1.66666…(1-x)^{0.6}+1.66666…

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integral from 0 to x of 1/((1-x)^{0.4)}

\int_{0}^{x} \frac{1}{( 1 - x ) ^{0.4}} d x

- 1.66666 \dots (1 - x)^{0.6} + 1.66666 \dots

Solution steps

\int_{0}^{x} \frac{1}{( 1 - x ) ^{0.4}} d x

Apply u-substitution

: \int_{1}^{1 - x} - \frac{1}{u ^{0.4}} d u

= \int_{1}^{1 - x} - \frac{1}{u ^{0.4}} 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 ^{0.4}} d u

Apply the Power Rule

: [1.66666 \dots u^{0.6}]_{1}^{1 - x}

= - [1.66666 \dots u^{0.6}]_{1}^{1 - x}

Compute the boundaries:

1.66666 \dots (1 - x)^{0.6} - 1.66666 \dots

= - (1.66666 \dots (1 - x)^{0.6} - 1.66666 \dots)

Simplify

= - 1.66666 \dots (1 - x)^{0.6} + 1.66666 \dots

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What is the integral from 0 to x of 1/((1-x)^{0.4)} ?
The integral from 0 to x of 1/((1-x)^{0.4)} is -1.66666…(1-x)^{0.6}+1.66666…