What is the integral from 0 to sqrt(3 of) 1/(x^2+1) ?

The integral from 0 to sqrt(3 of) 1/(x^2+1) is pi/3

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integral from 0 to sqrt(3 of) 1/(x^2+1)

\int_{0}^{3} \frac{1}{x ^{2} + 1} d x

\frac{π}{3}

Decimal Notation

1.04719 \dots

Solution steps

\int_{0}^{3} \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= [arctan (x)]_{0}^{3}

Compute the boundaries:

\frac{π}{3}

= \frac{π}{3}

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

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What is the integral from 0 to sqrt(3 of) 1/(x^2+1) ?
The integral from 0 to sqrt(3 of) 1/(x^2+1) is pi/3