What is the integral of ((ln(z))^7)/z ?

The integral of ((ln(z))^7)/z is (ln^8(z))/8+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((ln(z))^7)/z

\int \frac{( ln ( z ) ) ^{7}}{z} d z

\frac{ln ^{8} ( z )}{8} + C

Solution steps

\int \frac{( ln ( z ) ) ^{7}}{z} d z

Apply u-substitution

: \int u^{7} d u

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{u ^{8}}{8}

Substitute back

u = ln (z)

= \frac{ln ^{8} ( z )}{8}

Add a constant to the solution

= \frac{ln ^{8} ( z )}{8} + C

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

\int (4 - x^{2})^{- \frac{3}{2}} d x

\int (cot (x) + tan (x))^{2} d x

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

What is the integral of ((ln(z))^7)/z ?
The integral of ((ln(z))^7)/z is (ln^8(z))/8+C