What is the integral of ((ln(x))^{28})/x ?

The integral of ((ln(x))^{28})/x is (ln^{29}(x))/(29)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ((ln(x))^{28})/x

\int \frac{( ln ( x ) ) ^{28}}{x} d x

\frac{ln ^{29} ( x )}{29} + C

Solution steps

\int \frac{( ln ( x ) ) ^{28}}{x} d x

Apply u-substitution

= \int u^{28} d u

Apply the Power Rule

= \frac{u ^{29}}{29}

Substitute back

u = ln (x)

= \frac{ln ^{29} ( x )}{29}

Add a constant to the solution

= \frac{ln ^{29} ( x )}{29} + C

What is the integral of ((ln(x))^{28})/x ?
The integral of ((ln(x))^{28})/x is (ln^{29}(x))/(29)+C