What is the integral of (5x^4+6x-8) ?

The integral of (5x^4+6x-8) is x^5+3x^2-8x+C

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integral of (5x^4+6x-8)

\int (5 x^{4} + 6 x - 8) d x

x^{5} + 3 x^{2} - 8 x + C

Solution steps

\int 5 x^{4} + 6 x - 8 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 8 d x

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

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

\int 8 d x = 8 x

= x^{5} + 3 x^{2} - 8 x

Add a constant to the solution

= x^{5} + 3 x^{2} - 8 x + C

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What is the integral of (5x^4+6x-8) ?
The integral of (5x^4+6x-8) is x^5+3x^2-8x+C