What is the integral of ((ln(x))^{20})/x ?

The integral of ((ln(x))^{20})/x is (ln^{21}(x))/(21)+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))^{20})/x

\int \frac{( ln ( x ) ) ^{20}}{x} d x

\frac{ln ^{21} ( x )}{21} + C

Solution steps

\int \frac{( ln ( x ) ) ^{20}}{x} d x

Apply u-substitution

: \int u^{20} d u

= \int u^{20} d u

Apply the Power Rule

: \frac{u ^{21}}{21}

= \frac{u ^{21}}{21}

Substitute back

u = ln (x)

= \frac{ln ^{21} ( x )}{21}

Add a constant to the solution

= \frac{ln ^{21} ( x )}{21} + C

\frac{d}{d x} (arccos (5 x))

\frac{\partial}{\partial x} (4 - x^{2} - 2 y)

\int (\frac{1}{4 x ^{2}}) d x

9 x, \frac{3}{4} x, 70 - x^{2}

g (x) = 3 x^{2} lo g_{3} (x)

What is the integral of ((ln(x))^{20})/x ?
The integral of ((ln(x))^{20})/x is (ln^{21}(x))/(21)+C