What is the integral of (x^5)/(x^6-7) ?

The integral of (x^5)/(x^6-7) is 1/6 ln|x^6-7|+C

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integral of (x^5)/(x^6-7)

\int \frac{x ^{5}}{x ^{6} - 7} d x

\frac{1}{6} ln x^{6} - 7 + C

Solution steps

\int \frac{x ^{5}}{x ^{6} - 7} 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} - 7

= \frac{1}{6} ln x^{6} - 7

Add a constant to the solution

= \frac{1}{6} ln x^{6} - 7 + C

f (x) = arccos (4 x^{2})

θ \to 0 lim (\frac{1}{11})

sin^{2} (x)

x \to 0 + lim (\frac{2 ^{x}}{3 ^{x} - 1})

\frac{d}{d x} ((x + 2 x) e^{x})

What is the integral of (x^5)/(x^6-7) ?
The integral of (x^5)/(x^6-7) is 1/6 ln|x^6-7|+C