What is the integral of-10x^4+8x^3 ?

The integral of-10x^4+8x^3 is -2x^5+2x^4+C

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integral of-10x^4+8x^3

\int - 10 x^{4} + 8 x^{3} d x

- 2 x^{5} + 2 x^{4} + C

Solution steps

\int - 10 x^{4} + 8 x^{3} 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 10 x^{4} d x + \int 8 x^{3} d x

\int 10 x^{4} d x = 2 x^{5}

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

= - 2 x^{5} + 2 x^{4}

Add a constant to the solution

= - 2 x^{5} + 2 x^{4} + C

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