What is the integral of ((ln(x))^{30})/x ?

The integral of ((ln(x))^{30})/x is (ln^{31}(x))/(31)+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))^{30})/x

\int \frac{( ln ( x ) ) ^{30}}{x} d x

\frac{ln ^{31} ( x )}{31} + C

Solution steps

\int \frac{( ln ( x ) ) ^{30}}{x} d x

Apply u-substitution

: \int u^{30} d u

= \int u^{30} d u

Apply the Power Rule

: \frac{u ^{31}}{31}

= \frac{u ^{31}}{31}

Substitute back

u = ln (x)

= \frac{ln ^{31} ( x )}{31}

Add a constant to the solution

= \frac{ln ^{31} ( x )}{31} + C

\frac{d}{d x} (x^{3} - 3 x^{2} - 9 x + 3)

\int \frac{6 x - 5}{3 x ^{2} - 5 x} d x

\int_{36}^{x} 1 + 9 t d t

\frac{d}{d x} (ln (x^{4} + 1))

\frac{d}{d x} (9 x^{2} sin (x) tan (x))

What is the integral of ((ln(x))^{30})/x ?
The integral of ((ln(x))^{30})/x is (ln^{31}(x))/(31)+C