What is the integral of 5x^4-4x^5 ?

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

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integral of 5x^4-4x^5

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

x^{5} - \frac{2 x ^{6}}{3} + C

Solution steps

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

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

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

= x^{5} - \frac{2 x ^{6}}{3}

Add a constant to the solution

= x^{5} - \frac{2 x ^{6}}{3} + C