What is the integral of (3(ln(x))^2)/x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3(ln(x))^2)/x

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

ln^{3} (x) + C

Solution steps

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

Take the constant out:

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

= 3 \cdot \int \frac{( ln ( x ) ) ^{2}}{x} d x

Apply u-substitution

: \int u^{2} d u

= 3 \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= 3 \cdot \frac{u ^{3}}{3}

Substitute back

u = ln (x)

= 3 \cdot \frac{ln ^{3} ( x )}{3}

Simplify

3 \cdot \frac{ln ^{3} ( x )}{3} : ln^{3} (x)

= ln^{3} (x)

Add a constant to the solution

= ln^{3} (x) + C

\int 2 x (x^{2} + 8)^{9} d x

\int (csc (x))^{4} d x

\int \frac{t}{t} d t

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

\int \frac{5}{e ^{3 x}} d x

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