What is the integral from 0 to 3 of 5/(x^2+1) ?

The integral from 0 to 3 of 5/(x^2+1) is 5arctan(3)

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integral from 0 to 3 of 5/(x^2+1)

\int_{0}^{3} \frac{5}{x ^{2} + 1} d x

5 arctan (3)

Decimal

6.24522 \dots

Solution steps

\int_{0}^{3} \frac{5}{x ^{2} + 1} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{3} \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= 5 [arctan (x)]_{0}^{3}

Compute the boundaries:

arctan (3)

= 5 arctan (3)

What is the integral from 0 to 3 of 5/(x^2+1) ?
The integral from 0 to 3 of 5/(x^2+1) is 5arctan(3)