What is the integral of te^{t-1} ?

The integral of te^{t-1} is e^{t-1}t-e^{t-1}+C

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integral of te^{t-1}

\int t e^{t - 1} d t

e^{t - 1} t - e^{t - 1} + C

Solution steps

\int t e^{t - 1} d t

Apply Integration By Parts

: e^{t - 1} t - \int e^{t - 1} d t

= e^{t - 1} t - \int e^{t - 1} d t

\int e^{t - 1} d t = e^{t - 1}

= e^{t - 1} t - e^{t - 1}

Add a constant to the solution

= e^{t - 1} t - e^{t - 1} + C

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What is the integral of te^{t-1} ?
The integral of te^{t-1} is e^{t-1}t-e^{t-1}+C