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

The integral from-2 to 2 of (x+|x|)/(2+x^2) is ln(3)

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

\int_{- 2}^{2} \frac{x + ∣ x ∣}{2 + x ^{2}} d x

ln (3)

Decimal

1.09861 \dots

Solution steps

\int_{- 2}^{2} \frac{x + ∣ x ∣}{2 + x ^{2}} d x

Eliminate Absolutes

= \int_{- 2}^{0} \frac{x - x}{2 + x ^{2}} d x + \int_{0}^{2} \frac{x + x}{2 + x ^{2}} d x

\int_{- 2}^{0} \frac{x - x}{2 + x ^{2}} d x = 0

\int_{0}^{2} \frac{x + x}{2 + x ^{2}} d x = ln (3)

= 0 + ln (3)

Simplify

= ln (3)

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