What is the integral of x^9(5+x^{10}) ?

The integral of x^9(5+x^{10}) is (x^{10})/2+(x^{20})/(20)+C

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integral of x^9(5+x^{10})

\int x^{9} (5 + x^{10}) d x

\frac{x ^{10}}{2} + \frac{x ^{20}}{20} + C

Solution steps

\int x^{9} (5 + x^{10}) d x

Expand

x^{9} (5 + x^{10}) : 5 x^{9} + x^{19}

= \int 5 x^{9} + x^{19} 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^{9} d x + \int x^{19} d x

\int 5 x^{9} d x = \frac{x ^{10}}{2}

\int x^{19} d x = \frac{x ^{20}}{20}

= \frac{x ^{10}}{2} + \frac{x ^{20}}{20}

Add a constant to the solution

= \frac{x ^{10}}{2} + \frac{x ^{20}}{20} + C

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What is the integral of x^9(5+x^{10}) ?
The integral of x^9(5+x^{10}) is (x^{10})/2+(x^{20})/(20)+C