What is the integral from-1 to 1 of (x+1)e^{|x|} ?

The integral from-1 to 1 of (x+1)e^{|x|} is -2+2e

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integral from-1 to 1 of (x+1)e^{|x|}

\int_{- 1}^{1} (x + 1) e^{∣ x ∣} d x

- 2 + 2 e

Decimal

3.43656 \dots

Solution steps

\int_{- 1}^{1} (x + 1) e^{∣ x ∣} d x

Eliminate Absolutes

= \int_{- 1}^{0} (x + 1) e^{- x} d x + \int_{0}^{1} (x + 1) e^{x} d x

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

\int_{0}^{1} (x + 1) e^{x} d x = e

= - 2 + e + e

Simplify

= - 2 + 2 e

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What is the integral from-1 to 1 of (x+1)e^{|x|} ?
The integral from-1 to 1 of (x+1)e^{|x|} is -2+2e