What is the integral of (5x^4+8)/(x^5+8x) ?

The integral of (5x^4+8)/(x^5+8x) is ln|x^5+8x|+C

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integral of (5x^4+8)/(x^5+8x)

\int \frac{5 x ^{4} + 8}{x ^{5} + 8 x} d x

ln x^{5} + 8 x + C

Solution steps

\int \frac{5 x ^{4} + 8}{x ^{5} + 8 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} + 8 x

= ln x^{5} + 8 x

Add a constant to the solution

= ln x^{5} + 8 x + C

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\int_{1}^{9} \frac{2}{x} d x

\frac{d}{d x} (- 3 csc (x^{\frac{2}{3}}))

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What is the integral of (5x^4+8)/(x^5+8x) ?
The integral of (5x^4+8)/(x^5+8x) is ln|x^5+8x|+C