What is the integral of (x^5)/(x^6-2) ?

The integral of (x^5)/(x^6-2) is 1/6 ln|x^6-2|+C

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integral of (x^5)/(x^6-2)

\int \frac{x ^{5}}{x ^{6} - 2} d x

\frac{1}{6} ln x^{6} - 2 + C

Solution steps

\int \frac{x ^{5}}{x ^{6} - 2} 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} - 2

= \frac{1}{6} ln x^{6} - 2

Add a constant to the solution

= \frac{1}{6} ln x^{6} - 2 + C

\frac{d}{d x} (e^{x} (cos (x) - sin (x)))

y^{^{'}} = sin^{2} (x - y)

\frac{d}{d x} (\frac{3 x - 4}{12 x ^{2}})

F (x) = x + 1

y^{^{'}} = \frac{( x ^{2} - y ^{2} )}{x y}, y (2) = 2

What is the integral of (x^5)/(x^6-2) ?
The integral of (x^5)/(x^6-2) is 1/6 ln|x^6-2|+C