What is the integral of (4x^3+8x+9) ?

The integral of (4x^3+8x+9) is x^4+4x^2+9x+C

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integral of (4x^3+8x+9)

\int (4 x^{3} + 8 x + 9) d x

x^{4} + 4 x^{2} + 9 x + C

Solution steps

\int 4 x^{3} + 8 x + 9 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 8 x d x + \int 9 d x

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

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

\int 9 d x = 9 x

= x^{4} + 4 x^{2} + 9 x

Add a constant to the solution

= x^{4} + 4 x^{2} + 9 x + C

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What is the integral of (4x^3+8x+9) ?
The integral of (4x^3+8x+9) is x^4+4x^2+9x+C