What is the integral of e^{ln|x|} ?

The integral of e^{ln|x|} is (x|x|)/2+C

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integral of e^{ln|x|}

\int e^{l n ∣ x ∣} d x

\frac{x ∣ x ∣}{2} + C

Solution steps

\int e^{l n ∣ x ∣} d x

Apply log rule:

a^{l o g_{a} (b)} = b

= \int ∣ x ∣ d x

Use the common integral:

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= \frac{x ∣ x ∣}{2}

Add a constant to the solution

= \frac{x ∣ x ∣}{2} + C

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