What is the integral of (6u^2+12u) ?

The integral of (6u^2+12u) is 2u^3+6u^2+C

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integral of (6u^2+12u)

\int (6 u^{2} + 12 u) d u

2 u^{3} + 6 u^{2} + C

Solution steps

\int 6 u^{2} + 12 u d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 u^{2} d u + \int 12 u d u

\int 6 u^{2} d u = 2 u^{3}

\int 12 u d u = 6 u^{2}

= 2 u^{3} + 6 u^{2}

Add a constant to the solution

= 2 u^{3} + 6 u^{2} + C