What is the integral of 3arctan(3x) ?

The integral of 3arctan(3x) is 3(xarctan(3x)-1/6 ln|9x^2+1|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3arctan(3x)

\int 3 arctan (3 x) d x

3 (x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1) + C

Solution steps

\int 3 arctan (3 x) d x

Take the constant out:

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

= 3 \cdot \int arctan (3 x) d x

Apply Integration By Parts

: x arctan (3 x) - \int \frac{3 x}{9 x ^{2} + 1} d x

= 3 (x arctan (3 x) - \int \frac{3 x}{9 x ^{2} + 1} d x)

\int \frac{3 x}{9 x ^{2} + 1} d x = \frac{1}{6} ln 9 x^{2} + 1

= 3 (x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1)

Add a constant to the solution

= 3 (x arctan (3 x) - \frac{1}{6} ln 9 x^{2} + 1) + C

\int (3 x - 4)^{6} d x

\int 5 sin (x) - 4 cos (x) d x

\int \frac{5}{5 x + 3} d x

\int \frac{1}{4 sin ^{2} ( x ) + 9 cos ^{2} ( x )} d x

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

What is the integral of 3arctan(3x) ?
The integral of 3arctan(3x) is 3(xarctan(3x)-1/6 ln|9x^2+1|)+C