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Popular >

integral of x^5(x-9)

Solution

\int x^{5} (x - 9) d x

Solution

\frac{x ^{7}}{7} - \frac{3 x ^{6}}{2} + C

Solution steps

\int x^{5} (x - 9) d x

Expand

x^{5} (x - 9) : x^{6} - 9 x^{5}

= \int x^{6} - 9 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 x^{6} d x - \int 9 x^{5} d x

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

\int 9 x^{5} d x = \frac{3 x ^{6}}{2}

= \frac{x ^{7}}{7} - \frac{3 x ^{6}}{2}

Add a constant to the solution

= \frac{x ^{7}}{7} - \frac{3 x ^{6}}{2} + C

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Frequently Asked Questions (FAQ)

What is the integral of x^5(x-9) ?
The integral of x^5(x-9) is (x^7)/7-(3x^6)/2+C