What is the integral of e^{ln(5x)} ?

The integral of e^{ln(5x)} is 5x^2-(5x^2)/2+C

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integral of e^{ln(5x)}

\int e^{l n (5 x)} d x

5 x^{2} - \frac{5 x ^{2}}{2} + C

Solution steps

\int e^{l n (5 x)} d x

Apply Integration By Parts

: 5 x^{2} - \int 5 x d x

= 5 x^{2} - \int 5 x d x

\int 5 x d x = \frac{5 x ^{2}}{2}

= 5 x^{2} - \frac{5 x ^{2}}{2}

Add a constant to the solution

= 5 x^{2} - \frac{5 x ^{2}}{2} + C

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What is the integral of e^{ln(5x)} ?
The integral of e^{ln(5x)} is 5x^2-(5x^2)/2+C