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

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+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

x \to 9 lim (\frac{1}{( x - 9 ) ^{3}})

7 cos (7 x), 7 - 7 cos (7 x)

\int sec^{9} (x) tan (x) d x

\frac{d}{d x} (sin (π \cdot x))

\frac{d}{d x} (\frac{7}{x + 8})

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