What is the integral of (t+7)e^{2t+3} ?

The integral of (t+7)e^{2t+3} is 1/2 e^{2t+3}t+13/4 e^{2t+3}+C

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integral of (t+7)e^{2t+3}

\int (t + 7) e^{2 t + 3} d t

\frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3} + C

Solution steps

\int (t + 7) e^{2 t + 3} d t

Apply Integration By Parts

: \frac{1}{2} e^{2 t + 3} (t + 7) - \int \frac{1}{2} e^{2 t + 3} d t

= \frac{1}{2} e^{2 t + 3} (t + 7) - \int \frac{1}{2} e^{2 t + 3} d t

\int \frac{1}{2} e^{2 t + 3} d t = \frac{1}{4} e^{2 t + 3}

= \frac{1}{2} e^{2 t + 3} (t + 7) - \frac{1}{4} e^{2 t + 3}

Simplify

\frac{1}{2} e^{2 t + 3} (t + 7) - \frac{1}{4} e^{2 t + 3} : \frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3}

= \frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3}

Add a constant to the solution

= \frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3} + C

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What is the integral of (t+7)e^{2t+3} ?
The integral of (t+7)e^{2t+3} is 1/2 e^{2t+3}t+13/4 e^{2t+3}+C