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

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

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integral of e^{ln|t|}

\int e^{l n ∣ t ∣} d t

\frac{t ∣ t ∣}{2} + C

Solution steps

\int e^{l n ∣ t ∣} d t

Apply log rule:

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

= \int ∣ t ∣ d t

Use the common integral:

\int ∣ t ∣ d t = \frac{t ∣ t ∣}{2}

= \frac{t ∣ t ∣}{2}

Add a constant to the solution

= \frac{t ∣ t ∣}{2} + C