What is the integral of 18x+36x^2 ?

The integral of 18x+36x^2 is 9x^2+12x^3+C

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integral of 18x+36x^2

\int 18 x + 36 x^{2} d x

9 x^{2} + 12 x^{3} + C

Solution steps

\int 18 x + 36 x^{2} d x

Apply the Sum Rule:

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

= \int 18 x d x + \int 36 x^{2} d x

\int 18 x d x = 9 x^{2}

\int 36 x^{2} d x = 12 x^{3}

= 9 x^{2} + 12 x^{3}

Add a constant to the solution

= 9 x^{2} + 12 x^{3} + C