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

The integral of ln^2(3x) is xln^2(3x)-2(xln(3x)-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^2(3x)

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

x ln^{2} (3 x) - 2 (x ln (3 x) - x) + C

Solution steps

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

Apply Integration By Parts

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

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

\int 2 ln (3 x) d x = 2 (x ln (3 x) - x)

= x ln^{2} (3 x) - 2 (x ln (3 x) - x)

Add a constant to the solution

= x ln^{2} (3 x) - 2 (x ln (3 x) - x) + C

\int \frac{4 x + 3}{4 x ^{2} + 6 x - 1} d x

\int \frac{sin ( 2 x )}{1 + cos ( 2 x )} d x

\int csch (\frac{1}{2}) x coth (\frac{1}{2}) x d x

\int cos^{6} (8 x) sin (8 x) d x

\int \frac{1}{( x + x )} d x

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