What is the integral of s^2e^{3s} ?

The integral of s^2e^{3s} is 1/3 e^{3s}s^2-2/27 (3e^{3s}s-e^{3s})+C

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integral of s^2e^{3s}

\int s^{2} e^{3 s} d s

\frac{1}{3} e^{3 s} s^{2} - \frac{2}{27} (3 e^{3 s} s - e^{3 s}) + C

Solution steps

\int s^{2} e^{3 s} d s

Apply Integration By Parts

: \frac{1}{3} e^{3 s} s^{2} - \int \frac{2}{3} e^{3 s} s d s

= \frac{1}{3} e^{3 s} s^{2} - \int \frac{2}{3} e^{3 s} s d s

\int \frac{2}{3} e^{3 s} s d s = \frac{2}{27} (3 e^{3 s} s - e^{3 s})

= \frac{1}{3} e^{3 s} s^{2} - \frac{2}{27} (3 e^{3 s} s - e^{3 s})

Add a constant to the solution

= \frac{1}{3} e^{3 s} s^{2} - \frac{2}{27} (3 e^{3 s} s - e^{3 s}) + C

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What is the integral of s^2e^{3s} ?
The integral of s^2e^{3s} is 1/3 e^{3s}s^2-2/27 (3e^{3s}s-e^{3s})+C