What is the integral of e^{ln(3x)} ?

The integral of e^{ln(3x)} is 3x^2-(3x^2)/2+C

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integral of e^{ln(3x)}

\int e^{l n (3 x)} d x

3 x^{2} - \frac{3 x ^{2}}{2} + C

Solution steps

\int e^{l n (3 x)} d x

Apply Integration By Parts

= 3 x^{2} - \int 3 x d x

\int 3 x d x = \frac{3 x ^{2}}{2}

= 3 x^{2} - \frac{3 x ^{2}}{2}

Add a constant to the solution

= 3 x^{2} - \frac{3 x ^{2}}{2} + C

What is the integral of e^{ln(3x)} ?
The integral of e^{ln(3x)} is 3x^2-(3x^2)/2+C