What is the integral from 0 to 1 of 2arctan(x) ?

The integral from 0 to 1 of 2arctan(x) is pi/2-ln(2)

Popular >

integral from 0 to 1 of 2arctan(x)

\int_{0}^{1} 2 arctan (x) d x

\frac{π}{2} - ln (2)

Solution steps

\int_{0}^{1} 2 arctan (x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{1} arctan (x) d x

Apply Integration By Parts

: [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{1}

= 2 [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{1}

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

= 2 [x arctan (x) - \frac{1}{2} ln x^{2} + 1]_{0}^{1}

Compute the boundaries:

\frac{π}{4} - \frac{1}{2} ln (2)

= 2 (\frac{π}{4} - \frac{1}{2} ln (2))

Simplify

= \frac{π}{2} - ln (2)

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

\int_{0}^{\frac{π}{2}} (1 + cos (θ))^{2} d θ

\int_{- 3}^{- 2} \frac{2 - x}{32} d x

\int_{0}^{π} sin (e) d e

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

What is the integral from 0 to 1 of 2arctan(x) ?
The integral from 0 to 1 of 2arctan(x) is pi/2-ln(2)