What is the integral of (5x^4+6x+9) ?

The integral of (5x^4+6x+9) is x^5+3x^2+9x+C

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integral of (5x^4+6x+9)

\int (5 x^{4} + 6 x + 9) d x

x^{5} + 3 x^{2} + 9 x + C

Solution steps

\int 5 x^{4} + 6 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 5 x^{4} d x + \int 6 x d x + \int 9 d x

\int 5 x^{4} d x = x^{5}

\int 6 x d x = 3 x^{2}

\int 9 d x = 9 x

= x^{5} + 3 x^{2} + 9 x

Add a constant to the solution

= x^{5} + 3 x^{2} + 9 x + C

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What is the integral of (5x^4+6x+9) ?
The integral of (5x^4+6x+9) is x^5+3x^2+9x+C