What is the integral of (ln^9(x))/x ?

The integral of (ln^9(x))/x is (ln^{10}(x))/(10)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (ln^9(x))/x

\int \frac{ln ^{9} ( x )}{x} d x

\frac{ln ^{10} ( x )}{10} + C

Solution steps

\int \frac{ln ^{9} ( x )}{x} d x

Apply u-substitution

: \int u^{9} d u

= \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= \frac{u ^{10}}{10}

Substitute back

u = ln (x)

= \frac{ln ^{10} ( x )}{10}

Add a constant to the solution

= \frac{ln ^{10} ( x )}{10} + C

\int e^{x^{2}} x - e^{3 x^{4}} 12 x^{3} d x

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

\int \frac{8 x ^{3}}{x ^{4} + 7} d x

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

\int x^{3} y e^{x y} + 3 x^{2} e^{x y} d x

What is the integral of (ln^9(x))/x ?
The integral of (ln^9(x))/x is (ln^{10}(x))/(10)+C