What is the integral of 13x^2arctan(x) ?

The integral of 13x^2arctan(x) is 13(1/3 x^3arctan(x)-1/6 (x^2+1-ln|x^2+1|))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 13x^2arctan(x)

\int 13 x^{2} arctan (x) d x

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

Solution steps

\int 13 x^{2} arctan (x) d x

Take the constant out:

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

= 13 \cdot \int x^{2} arctan (x) d x

Apply Integration By Parts

= 13 (\frac{1}{3} x^{3} arctan (x) - \int \frac{x ^{3}}{3 ( x ^{2} + 1 )} d x)

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

= 13 (\frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1))

Add a constant to the solution

= 13 (\frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1)) + C

What is the integral of 13x^2arctan(x) ?
The integral of 13x^2arctan(x) is 13(1/3 x^3arctan(x)-1/6 (x^2+1-ln|x^2+1|))+C