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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of arctan(x/3)

\int arctan (\frac{x}{3}) d x

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

Solution steps

\int arctan (\frac{x}{3}) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int x^{9} x^{5} + 6 d x

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

\frac{3 x ^{2} - 1}{2 x x}

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

x \to 2 lim (\frac{1}{4 - x ^{2}})

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