What is the integral of (8x^3+3x^2) ?

The integral of (8x^3+3x^2) is 2x^4+x^3+C

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integral of (8x^3+3x^2)

\int (8 x^{3} + 3 x^{2}) d x

2 x^{4} + x^{3} + C

Solution steps

\int 8 x^{3} + 3 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 8 x^{3} d x + \int 3 x^{2} d x

\int 8 x^{3} d x = 2 x^{4}

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

= 2 x^{4} + x^{3}

Add a constant to the solution

= 2 x^{4} + x^{3} + C

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