What is the integral of (ln^4(x))/x ?

The integral of (ln^4(x))/x is (ln^5(x))/5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (ln^4(x))/x

\int \frac{ln ^{4} ( x )}{x} d x

\frac{ln ^{5} ( x )}{5} + C

Solution steps

\int \frac{ln ^{4} ( x )}{x} d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = ln (x)

= \frac{ln ^{5} ( x )}{5}

Add a constant to the solution

= \frac{ln ^{5} ( x )}{5} + C

\int \frac{x ^{3} - 2 x ^{2} + x + 1}{x ^{4} + 5 x ^{2} + 4} d x

\int \frac{4 sin ( x )}{x} d x

\int - 3 x^{2} + \frac{1}{x} d x

\int \frac{5}{x ( ln ( x ) ) ^{3}} d x

\int \frac{sec ^{2} ( x )}{25 - tan ^{2} ( x )} d x

What is the integral of (ln^4(x))/x ?
The integral of (ln^4(x))/x is (ln^5(x))/5+C