What is the integral of (x^5)/(x^6-4) ?

The integral of (x^5)/(x^6-4) is 1/6 ln|x^6-4|+C

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integral of (x^5)/(x^6-4)

\int \frac{x ^{5}}{x ^{6} - 4} d x

\frac{1}{6} ln x^{6} - 4 + C

Solution steps

\int \frac{x ^{5}}{x ^{6} - 4} 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} - 4

= \frac{1}{6} ln x^{6} - 4

Add a constant to the solution

= \frac{1}{6} ln x^{6} - 4 + C

\frac{d}{d x} (csc (x) tan (x))

4 sin (t) \frac{d y}{d t} + 4 y cos (t) = cos (t) sin^{4} (t)

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3 x} + x^{2}

x \to 0 lim (x^{2} - 2)

\frac{3}{x ^{2} - x - 2}, 1

What is the integral of (x^5)/(x^6-4) ?
The integral of (x^5)/(x^6-4) is 1/6 ln|x^6-4|+C