What is the integral of-5(x^4)/(1-x^5) ?

The integral of-5(x^4)/(1-x^5) is ln|1-x^5|+C

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integral of-5(x^4)/(1-x^5)

\int - 5 \frac{x ^{4}}{1 - x ^{5}} d x

ln 1 - x^{5} + C

Solution steps

\int - 5 \cdot \frac{x ^{4}}{1 - x ^{5}} d x

Take the constant out:

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

= - 5 \cdot \int \frac{x ^{4}}{1 - x ^{5}} d x

Apply u-substitution

: \int - \frac{1}{5 u} d u

= - 5 \cdot \int - \frac{1}{5 u} d u

Take the constant out:

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

= - 5 (- \frac{1}{5} \cdot \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 5 (- \frac{1}{5} ln ∣ u ∣)

Substitute back

u = 1 - x^{5}

= - 5 (- \frac{1}{5} ln 1 - x^{5})

Simplify

- 5 (- \frac{1}{5} ln 1 - x^{5}) : ln 1 - x^{5}

= ln 1 - x^{5}

Add a constant to the solution

= ln 1 - x^{5} + C

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What is the integral of-5(x^4)/(1-x^5) ?
The integral of-5(x^4)/(1-x^5) is ln|1-x^5|+C