What is the integral of z^2e^z ?

The integral of z^2e^z is z^2e^z-2(e^zz-e^z)+C

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integral of z^2e^z

\int z^{2} e^{z} d z

z^{2} e^{z} - 2 (e^{z} z - e^{z}) + C

Solution steps

\int z^{2} e^{z} d z

Apply Integration By Parts

: z^{2} e^{z} - \int 2 z e^{z} d z

= z^{2} e^{z} - \int 2 z e^{z} d z

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

= z^{2} e^{z} - 2 (e^{z} z - e^{z})

Add a constant to the solution

= z^{2} e^{z} - 2 (e^{z} z - e^{z}) + C

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