What is the integral from 0 to 10 of arctan(x) ?

The integral from 0 to 10 of arctan(x) is 10arctan(10)-1/2 ln(101)

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integral from 0 to 10 of arctan(x)

\int_{0}^{10} arctan (x) d x

10 arctan (10) - \frac{1}{2} ln (101)

Decimal Notation

12.40371 \dots

Solution steps

\int_{0}^{10} arctan (x) d x

Apply Integration By Parts

: [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{10}

= [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{10}

\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]_{0}^{10}

Compute the boundaries:

10 arctan (10) - \frac{1}{2} ln (101)

= 10 arctan (10) - \frac{1}{2} ln (101)

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What is the integral from 0 to 10 of arctan(x) ?
The integral from 0 to 10 of arctan(x) is 10arctan(10)-1/2 ln(101)