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

The integral of e^{t+ln(t)} is e^tt-e^t+C

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

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

e^{t} t - e^{t} + C

Solution steps

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

Simplify

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

= \int e^{t} t d t

Apply Integration By Parts

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

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

= e^{t} t - e^{t}

Add a constant to the solution

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