What is the integral of (x^5)/(x^6-3) ?

The integral of (x^5)/(x^6-3) is 1/6 ln|x^6-3|+C

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integral of (x^5)/(x^6-3)

\int \frac{x ^{5}}{x ^{6} - 3} d x

\frac{1}{6} ln x^{6} - 3 + C

Solution steps

\int \frac{x ^{5}}{x ^{6} - 3} d x

Apply u-substitution

: \int \frac{1}{6 u} d u

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} ln ∣ u ∣

Substitute back

u = x^{6} - 3

= \frac{1}{6} ln x^{6} - 3

Add a constant to the solution

= \frac{1}{6} ln x^{6} - 3 + C

f (x) = 9 e^{x} (cos (x) - sin (x))

\frac{d}{d x} (x^{4} sin (x) tan (x))

- 4 x^{2} + 7 x

n = 3 \sum \infty e^{5 - 4 n}

\int \frac{- x}{( x ^{2} + 1 ) ^{2}} d x

What is the integral of (x^5)/(x^6-3) ?
The integral of (x^5)/(x^6-3) is 1/6 ln|x^6-3|+C