What is the integral of arctan(ax) ?

The integral of arctan(ax) is xarctan(ax)-1/(2a)ln|a^2x^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 arctan(ax)

\int arctan (a x) d x

x arctan (a x) - \frac{1}{2 a} ln a^{2} x^{2} + 1 + C

Solution steps

\int arctan (a x) d x

Apply Integration By Parts

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

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

\int \frac{a x}{a ^{2} x ^{2} + 1} d x = \frac{1}{2 a} ln a^{2} x^{2} + 1

= x arctan (a x) - \frac{1}{2 a} ln a^{2} x^{2} + 1

Add a constant to the solution

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

x \to 3 lim (5^{2})

y = x^{2} + 2, y = x + 14

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

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

f (x) = \frac{7 x ^{2} - x + 9}{6 - 7 x}

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