What is the integral of (5x^4+2)/(x^5+2x) ?

The integral of (5x^4+2)/(x^5+2x) is ln|x^5+2x|+C

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integral of (5x^4+2)/(x^5+2x)

\int \frac{5 x ^{4} + 2}{x ^{5} + 2 x} d x

ln x^{5} + 2 x + C

Solution steps

\int \frac{5 x ^{4} + 2}{x ^{5} + 2 x} d x

Apply u-substitution

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

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{5} + 2 x

= ln x^{5} + 2 x

Add a constant to the solution

= ln x^{5} + 2 x + C

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What is the integral of (5x^4+2)/(x^5+2x) ?
The integral of (5x^4+2)/(x^5+2x) is ln|x^5+2x|+C