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

The integral of u^2e^u is u^2e^u-2(e^uu-e^u)+C

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integral of u^2e^u

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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