What is the integral from 1 to 5 of (x-arctan(x)) ?

The integral from 1 to 5 of (x-arctan(x)) is 12-5arctan(5)+1/2 ln(26)+pi/4-1/2 ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 5 of (x-arctan(x))

\int_{1}^{5} (x - arctan (x)) d x

12 - 5 arctan (5) + \frac{1}{2} ln (26) + \frac{π}{4} - \frac{1}{2} ln (2)

Solution steps

\int_{1}^{5} x - arctan (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{5} x d x - \int_{1}^{5} arctan (x) d x

\int_{1}^{5} x d x = 12

\int_{1}^{5} arctan (x) d x = 5 arctan (5) - \frac{1}{2} ln (26) - \frac{π}{4} + \frac{1}{2} ln (2)

= 12 - (5 arctan (5) - \frac{1}{2} ln (26) - \frac{π}{4} + \frac{1}{2} ln (2))

Simplify

= 12 - 5 arctan (5) + \frac{1}{2} ln (26) + \frac{π}{4} - \frac{1}{2} ln (2)

\int_{0}^{5} \frac{1}{x ^{\frac{8}{9}}} d x

\int_{1}^{e - 1} 2 x ln (x + 1) d x

\int_{- 4}^{3} x^{2} + x - 12 d x

\int_{- 4}^{4} (2 - x) d x

\int_{0}^{1} (x^{3} - x + 1) d x

What is the integral from 1 to 5 of (x-arctan(x)) ?
The integral from 1 to 5 of (x-arctan(x)) is 12-5arctan(5)+1/2 ln(26)+pi/4-1/2 ln(2)