What is the integral of 3u^2e^u ?

The integral of 3u^2e^u is 3(u^2e^u-2(e^uu-e^u))+C

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integral of 3u^2e^u

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int u^{2} e^{u} d u

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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