Question

(q35) Evaluate the integral

Answer 1

B. -1/2e^(-2x) +C

Explanation:

You want the indefinite integral of ln(e^(e^(-2x))).

Simplify

The integrand can be simplified using ln(e^x) = x:

ln(e^(e^(-2x))) = e^(-2x)

Integrate

The antiderivative of e^a is (1/a)e^a, so the integral of interest is ...

`\displaystyle \int{e^(-2x)}\,dx=(1)/(-2)e^(-2x)+C=\boxed{-(1)/(2)e^(-2x)+C}`

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