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

The integral of (((ln(x))^8)/x) is (ln^9(x))/9+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)/x)

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

\frac{ln ^{9} ( x )}{9} + C

Solution steps

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

Apply u-substitution

: \int u^{8} d u

= \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= \frac{u ^{9}}{9}

Substitute back

u = ln (x)

= \frac{ln ^{9} ( x )}{9}

Add a constant to the solution

= \frac{ln ^{9} ( x )}{9} + C

\int 5 ln (\frac{x}{5}) d x

\int \frac{x - 3}{3 x ^{2} + 6 x + 2} d x

\int (x^{2} + 2)^{3} x d x

\int \frac{5 x - 2}{( x + 2 ) ^{2}} d x

What is the integral of (((ln(x))^8)/x) ?
The integral of (((ln(x))^8)/x) is (ln^9(x))/9+C