What is the integral from 0 to pi of 2/(x^2+1) ?

The integral from 0 to pi of 2/(x^2+1) is 2arctan(pi)

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integral from 0 to pi of 2/(x^2+1)

\int_{0}^{π} \frac{2}{x ^{2} + 1} d x

2 arctan (π)

Decimal Notation

2.52525 \dots

Solution steps

\int_{0}^{π} \frac{2}{x ^{2} + 1} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{π} \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= 2 [arctan (x)]_{0}^{π}

Compute the boundaries:

arctan (π)

= 2 arctan (π)

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

\int_{0}^{\frac{1}{2}} 2 x^{2} + x d x

\int_{- 2}^{2} (4 - x^{2})^{3} d x

\int_{0}^{1} 1 - x^{2} x^{2} d x

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

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