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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int \frac{e ^{t}}{1 + e ^{2 t}} d t

x \to - 5 + lim (\frac{∣ x + 5 ∣}{x + 5})

\frac{d}{d x} (sin^{3} (2 x^{2}))

\int 4^{x} \cdot e^{2 x} d x

x \to 0 lim (x - 10 + 5 x)

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