What is the integral from-1 to 3 of x/(1+|x|) ?

The integral from-1 to 3 of x/(1+|x|) is -ln(2)+2

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integral from-1 to 3 of x/(1+|x|)

\int_{- 1}^{3} \frac{x}{1 + ∣ x ∣} d x

- ln (2) + 2

Solution steps

\int_{- 1}^{3} \frac{x}{1 + ∣ x ∣} d x

Eliminate Absolutes

= \int_{- 1}^{0} \frac{x}{1 - x} d x + \int_{0}^{3} \frac{x}{1 + x} d x

\int_{- 1}^{0} \frac{x}{1 - x} d x = - 1 + ln (2)

\int_{0}^{3} \frac{x}{1 + x} d x = 3 - 2 ln (2)

= - 1 + ln (2) + 3 - 2 ln (2)

Simplify

= - ln (2) + 2

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