What is the integral of ln(x^8) ?

The integral of ln(x^8) is 8xln(x)-8x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(x^8)

\int ln (x^{8}) d x

8 x ln (x) - 8 x + C

Solution steps

\int ln (x^{8}) d x

Apply Integration By Parts

: x ln (x^{8}) - \int 8 d x

= x ln (x^{8}) - \int 8 d x

\int 8 d x = 8 x

= x ln (x^{8}) - 8 x

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 8 x ln (x) - 8 x

Add a constant to the solution

= 8 x ln (x) - 8 x + C

\frac{d}{d x} (6^{6 - x^{2}})

y = - 2 x + 7

\int_{7}^{14} - 30 x^{2} + 420 x d x

\int \frac{1}{x ^{5} 9 x ^{2} - 1} d x

\int sin (2) (x) d x