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

The integral of e^{x+ln(x)} is e^xx-e^x+C

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

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

e^{x} x - e^{x} + C

Solution steps

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

Simplify

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

= \int e^{x} x d x

Apply Integration By Parts

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

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

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

= e^{x} x - e^{x}

Add a constant to the solution

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

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