What is the integral of xarctan(7x) ?

The integral of xarctan(7x) is 1/2 x^2arctan(7x)-1/98 (-arctan(7x)+7x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xarctan(7x)

\int x arctan (7 x) d x

\frac{1}{2} x^{2} arctan (7 x) - \frac{1}{98} (- arctan (7 x) + 7 x) + C

Solution steps

\int x arctan (7 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} arctan (7 x) - \int \frac{7 x ^{2}}{2 ( 49 x ^{2} + 1 )} d x

= \frac{1}{2} x^{2} arctan (7 x) - \int \frac{7 x ^{2}}{2 ( 49 x ^{2} + 1 )} d x

\int \frac{7 x ^{2}}{2 ( 49 x ^{2} + 1 )} d x = \frac{1}{98} (- arctan (7 x) + 7 x)

= \frac{1}{2} x^{2} arctan (7 x) - \frac{1}{98} (- arctan (7 x) + 7 x)

Add a constant to the solution

= \frac{1}{2} x^{2} arctan (7 x) - \frac{1}{98} (- arctan (7 x) + 7 x) + C

\frac{d y}{d t} = 5 - 2 y

\int sin (w x) d x

f (x) = 9 x^{3}

z \to 0 lim (\frac{sin ( z )}{z})

\int 2 + x d x

What is the integral of xarctan(7x) ?
The integral of xarctan(7x) is 1/2 x^2arctan(7x)-1/98 (-arctan(7x)+7x)+C