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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

\int x^{2} - x + 3 d x

\int 2 + sin (t) d t

\int \frac{1}{- 4 + x ^{2}} d x

\int e^{\frac{x}{a}} + e^{- \frac{x}{a}} d x

\int x (2 sin (x) + 4 sin^{2} (x)) d x

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