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

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

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

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

\frac{3 π}{4}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{4} - (- \frac{π}{2})

Simplify

= \frac{3 π}{4}

f (x) = 2 x - x^{2}

\int cos (x) sin^{5} (x) d x

3 - x, - 4 \leq x \leq 2

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

\frac{2}{x ^{7}}

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