What is the integral of 4x^3+4x+2 ?

The integral of 4x^3+4x+2 is x^4+2x^2+2x+C

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integral of 4x^3+4x+2

\int 4 x^{3} + 4 x + 2 d x

x^{4} + 2 x^{2} + 2 x + C

Solution steps

\int 4 x^{3} + 4 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 4 x^{3} d x + \int 4 x d x + \int 2 d x

\int 4 x^{3} d x = x^{4}

\int 4 x d x = 2 x^{2}

\int 2 d x = 2 x

= x^{4} + 2 x^{2} + 2 x

Add a constant to the solution

= x^{4} + 2 x^{2} + 2 x + C

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