What is the integral from-infinity to 3 of 1/(4+x^2) ?

The integral from-infinity to 3 of 1/(4+x^2) is 1/2 arctan(3/2)+pi/4

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integral from-infinity to 3 of 1/(4+x^2)

\int_{- \infty}^{3} \frac{1}{4 + x ^{2}} d x

\frac{1}{2} arctan (\frac{3}{2}) + \frac{π}{4}

Decimal

1.27679 \dots

Solution steps

\int_{- \infty}^{3} \frac{1}{4 + x ^{2}} d x

Compute the indefinite integral:

\int \frac{1}{4 + x ^{2}} d x = \frac{1}{2} arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{- \infty}^{3} \frac{1}{4 + x ^{2}} d x = \frac{1}{2} arctan (\frac{3}{2}) - (- \frac{π}{4})

= \frac{1}{2} arctan (\frac{3}{2}) - (- \frac{π}{4})

Simplify

= \frac{1}{2} arctan (\frac{3}{2}) + \frac{π}{4}

What is the integral from-infinity to 3 of 1/(4+x^2) ?
The integral from-infinity to 3 of 1/(4+x^2) is 1/2 arctan(3/2)+pi/4