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

The integral of ((ln(y))^4)/y is (ln^5(y))/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(y))^4)/y

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

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

Solution steps

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

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 (y)

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

Add a constant to the solution

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

\int e^{3 x} x cos (5 x) d x

\int \frac{1}{( x + 1 ) x + 6} d x

\int 1 d x^{- 1}

\int \frac{16}{x ^{4} 4 - x ^{2}} d x

\int 11 x + 12 x d x

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