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

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

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

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

2 (arctan (3) - arctan (2))

Decimal

0.28379 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= 2 [arctan (x)]_{2}^{3}

Compute the boundaries:

arctan (3) - arctan (2)

= 2 (arctan (3) - arctan (2))

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