What is the integral of s^3e^s ?

The integral of s^3e^s is s^3e^s-3(s^2e^s-2(e^ss-e^s))+C

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integral of s^3e^s

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

s^{3} e^{s} - 3 (s^{2} e^{s} - 2 (e^{s} s - e^{s})) + C

Solution steps

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

Apply Integration By Parts

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

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

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

= s^{3} e^{s} - 3 (s^{2} e^{s} - 2 (e^{s} s - e^{s}))

Add a constant to the solution

= s^{3} e^{s} - 3 (s^{2} e^{s} - 2 (e^{s} s - e^{s})) + C

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What is the integral of s^3e^s ?
The integral of s^3e^s is s^3e^s-3(s^2e^s-2(e^ss-e^s))+C