What is the integral of (18x^7)/(9x^8+9) ?

The integral of (18x^7)/(9x^8+9) is 1/4 ln|9x^8+9|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (18x^7)/(9x^8+9)

\int \frac{18 x ^{7}}{9 x ^{8} + 9} d x

\frac{1}{4} ln 9 x^{8} + 9 + C

Solution steps

\int \frac{18 x ^{7}}{9 x ^{8} + 9} d x

Take the constant out:

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

= 18 \cdot \int \frac{x ^{7}}{9 x ^{8} + 9} d x

Apply u-substitution

: \int \frac{1}{72 u} d u

= 18 \cdot \int \frac{1}{72 u} d u

Take the constant out:

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

= 18 \cdot \frac{1}{72} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 18 \cdot \frac{1}{72} ln ∣ u ∣

Substitute back

u = 9 x^{8} + 9

= 18 \cdot \frac{1}{72} ln 9 x^{8} + 9

Simplify

18 \cdot \frac{1}{72} ln 9 x^{8} + 9 : \frac{1}{4} ln 9 x^{8} + 9

= \frac{1}{4} ln 9 x^{8} + 9

Add a constant to the solution

= \frac{1}{4} ln 9 x^{8} + 9 + C

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

\int \frac{x ^{4}}{1 - 25 x ^{10}} d x

\int \frac{2}{x} + \frac{x}{2} d x

\int (3 sec^{2} (x) - 2 csc^{2} (x)) d x

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

What is the integral of (18x^7)/(9x^8+9) ?
The integral of (18x^7)/(9x^8+9) is 1/4 ln|9x^8+9|+C