What is the integral of (ln^5(x^2))/x ?

The integral of (ln^5(x^2))/x is 16/3 ln^6(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (ln^5(x^2))/x

\int \frac{ln ^{5} ( x ^{2} )}{x} d x

\frac{16}{3} ln^{6} (x) + C

Solution steps

\int \frac{ln ^{5} ( x ^{2} )}{x} d x

Apply u-substitution

: \int \frac{ln ^{5} ( u )}{2 u} d u

= \int \frac{ln ^{5} ( u )}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{ln ^{5} ( u )}{u} d u

Apply u-substitution

: \int v^{5} d v

= \frac{1}{2} \cdot \int v^{5} d v

Apply the Power Rule

: \frac{v ^{6}}{6}

= \frac{1}{2} \cdot \frac{v ^{6}}{6}

Substitute back

= \frac{1}{2} \cdot \frac{ln ^{6} ( x ^{2} )}{6}

Simplify

\frac{1}{2} \cdot \frac{ln ^{6} ( x ^{2} )}{6} : \frac{16}{3} ln^{6} (x)

= \frac{16}{3} ln^{6} (x)

Add a constant to the solution

= \frac{16}{3} ln^{6} (x) + C

\frac{d}{d x} (- 6 x^{2} + 6 x)

\int 2 (3 - e^{- t}) d t

\frac{2}{s ^{2} + 4 s + 3}

\frac{d}{d x} (- x^{2} sin (x^{2} y))

x \to 3 lim (x^{3} - 3 x^{2} - 9 x)

What is the integral of (ln^5(x^2))/x ?
The integral of (ln^5(x^2))/x is 16/3 ln^6(x)+C