What is the integral of (x^7)/(1+x^8) ?

The integral of (x^7)/(1+x^8) is 1/8 ln|1+x^8|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^7)/(1+x^8)

\int \frac{x ^{7}}{1 + x ^{8}} d x

\frac{1}{8} ln 1 + x^{8} + C

Solution steps

\int \frac{x ^{7}}{1 + x ^{8}} d x

Apply u-substitution

: \int \frac{1}{8 u} d u

= \int \frac{1}{8 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{8} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{8} ln ∣ u ∣

Substitute back

u = 1 + x^{8}

= \frac{1}{8} ln 1 + x^{8}

Add a constant to the solution

= \frac{1}{8} ln 1 + x^{8} + C

\int \frac{3 x + 8}{x ^{3} + 4 x} d x

\int (- 4 x^{3} + 6 x^{2} + 5 x - 5) d x

\int e^{2 q} cos (3 e^{q}) d q

\int \frac{1}{( 2 - x ) 1 - x ^{2}} d x

\int 11 csc^{2} (x) d x

What is the integral of (x^7)/(1+x^8) ?
The integral of (x^7)/(1+x^8) is 1/8 ln|1+x^8|+C