What is the integral of 4(x+2)^3-30x-6 ?

The integral of 4(x+2)^3-30x-6 is (x+2)^4-15x^2-6x+C

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integral of 4(x+2)^3-30x-6

\int 4 (x + 2)^{3} - 30 x - 6 d x

(x + 2)^{4} - 15 x^{2} - 6 x + C

Solution steps

\int 4 (x + 2)^{3} - 30 x - 6 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 4 (x + 2)^{3} d x - \int 30 x d x - \int 6 d x

\int 4 (x + 2)^{3} d x = (x + 2)^{4}

\int 30 x d x = 15 x^{2}

\int 6 d x = 6 x

= (x + 2)^{4} - 15 x^{2} - 6 x

Add a constant to the solution

= (x + 2)^{4} - 15 x^{2} - 6 x + C

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What is the integral of 4(x+2)^3-30x-6 ?
The integral of 4(x+2)^3-30x-6 is (x+2)^4-15x^2-6x+C