What is the integral of (x^5-x^3) ?

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

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integral of (x^5-x^3)

\int (x^{5} - x^{3}) d x

\frac{x ^{6}}{6} - \frac{x ^{4}}{4} + C

Solution steps

\int x^{5} - 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 x^{5} d x - \int x^{3} d x

\int x^{5} d x = \frac{x ^{6}}{6}

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

= \frac{x ^{6}}{6} - \frac{x ^{4}}{4}

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{x ^{4}}{4} + C

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