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Popular >

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

Solution

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

Solution

0

Solution steps

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

Eliminate Absolutes

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

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

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

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

Simplify

- 3 + 2 ln (2) + 3 - 2 ln (2) : 0

= 0

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Frequently Asked Questions (FAQ)

What is the integral from-3 to 3 of x/(1+|x|) ?
The integral from-3 to 3 of x/(1+|x|) is 0