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

The integral of (x^6+x^8) is (x^7)/7+(x^9)/9+C

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integral of (x^6+x^8)

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

\frac{x ^{7}}{7} + \frac{x ^{9}}{9} + C

Solution steps

\int x^{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 x^{6} d x + \int x^{8} d x

\int x^{6} d x = \frac{x ^{7}}{7}

\int x^{8} d x = \frac{x ^{9}}{9}

= \frac{x ^{7}}{7} + \frac{x ^{9}}{9}

Add a constant to the solution

= \frac{x ^{7}}{7} + \frac{x ^{9}}{9} + C

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What is the integral of (x^6+x^8) ?
The integral of (x^6+x^8) is (x^7)/7+(x^9)/9+C