What is the integral of ln(e^{4x}) ?

The integral of ln(e^{4x}) is 2x^2+C

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integral of ln(e^{4x})

\int ln (e^{4 x}) d x

2 x^{2} + C

Solution steps

\int ln (e^{4 x}) d x

Apply Integration By Parts

= 4 x^{2} - \int 4 x d x

\int 4 x d x = 2 x^{2}

= 4 x^{2} - 2 x^{2}

Simplify

= 2 x^{2}

Add a constant to the solution

= 2 x^{2} + C

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