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

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

Popular >

integral from 1 to 2 of arctan(x)

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

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

Decimal Notation

0.97075 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

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

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

\int_{- 0.5}^{0.5} 8 x^{2} - 2 d x

\int_{0}^{0.8} 48000 x - 21600 d x

\int_{0}^{π} 2 - 2 cos (x) d x

\int_{1}^{x} sin (t) d t

\int_{0}^{1} (3 x)^{2} - (3 x^{2})^{2} d x

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