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Popular >

integral of ln(2e^x)

Solution

\int ln (2 e^{x}) d x

Solution

ln (2) x + \frac{x ^{2}}{2} + C

Solution steps

\int ln (2 e^{x}) d x

Simplify

ln (2 e^{x}) : ln (2) + x

= \int ln (2) + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int ln (2) d x + \int x d x

\int ln (2) d x = ln (2) x

\int x d x = \frac{x ^{2}}{2}

= ln (2) x + \frac{x ^{2}}{2}

Add a constant to the solution

= ln (2) x + \frac{x ^{2}}{2} + C

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Frequently Asked Questions (FAQ)

What is the integral of ln(2e^x) ?
The integral of ln(2e^x) is ln(2)x+(x^2)/2+C