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

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

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integral of (x^5)/(x^6+6)

\int \frac{x ^{5}}{x ^{6} + 6} d x

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

Solution steps

\int \frac{x ^{5}}{x ^{6} + 6} 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} + 6

= \frac{1}{6} ln x^{6} + 6

Add a constant to the solution

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

x \to - 1 lim (\frac{x ^{2}}{x + 1})

\frac{\partial}{\partial x} (ln (ln (2 x + 2 y)))

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

\int_{0}^{π} x cos (n x) d x

\frac{s + 1}{s ( s ^{2} + 2 s + 5 )}

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