What is the integral of e^{ln(y)+y} ?

The integral of e^{ln(y)+y} is e^yy-e^y+C

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integral of e^{ln(y)+y}

\int e^{l n (y) + y} d y

e^{y} y - e^{y} + C

Solution steps

\int e^{l n (y) + y} d y

Simplify

e^{l n (y) + y} : e^{y} y

= \int e^{y} y d y

Apply Integration By Parts

: e^{y} y - \int e^{y} d y

= e^{y} y - \int e^{y} d y

\int e^{y} d y = e^{y}

= e^{y} y - e^{y}

Add a constant to the solution

= e^{y} y - e^{y} + C

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