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Popular >

integral of (x+9)^8(x+5)

Solution

\int (x + 9)^{8} (x + 5) d x

Solution

\frac{x ^{10}}{10} + \frac{77 x ^{9}}{9} + \frac{657 x ^{8}}{2} + 7452 x^{7} + 110565 x^{6} + \frac{5603094 x ^{5}}{5} + 7853517 x^{4} + 37555164 x^{3} + \frac{234365481 x ^{2}}{2} + 215233605 x + C

Solution steps

\int (x + 9)^{8} (x + 5) d x

Expand

(x + 9)^{8} (x + 5) : x^{9} + 77 x^{8} + 2628 x^{7} + 52164 x^{6} + 663390 x^{5} + 5603094 x^{4} + 31414068 x^{3} + 112665492 x^{2} + 234365481 x + 215233605

= \int x^{9} + 77 x^{8} + 2628 x^{7} + 52164 x^{6} + 663390 x^{5} + 5603094 x^{4} + 31414068 x^{3} + 112665492 x^{2} + 234365481 x + 215233605 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^{9} d x + \int 77 x^{8} d x + \int 2628 x^{7} d x + \int 52164 x^{6} d x + \int 663390 x^{5} d x + \int 5603094 x^{4} d x + \int 31414068 x^{3} d x + \int 112665492 x^{2} d x + \int 234365481 x d x + \int 215233605 d x

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

\int 77 x^{8} d x = \frac{77 x ^{9}}{9}

\int 2628 x^{7} d x = \frac{657 x ^{8}}{2}

\int 52164 x^{6} d x = 7452 x^{7}

\int 663390 x^{5} d x = 110565 x^{6}

\int 5603094 x^{4} d x = \frac{5603094 x ^{5}}{5}

\int 31414068 x^{3} d x = 7853517 x^{4}

\int 112665492 x^{2} d x = 37555164 x^{3}

\int 234365481 x d x = \frac{234365481 x ^{2}}{2}

\int 215233605 d x = 215233605 x

= \frac{x ^{10}}{10} + \frac{77 x ^{9}}{9} + \frac{657 x ^{8}}{2} + 7452 x^{7} + 110565 x^{6} + \frac{5603094 x ^{5}}{5} + 7853517 x^{4} + 37555164 x^{3} + \frac{234365481 x ^{2}}{2} + 215233605 x

Add a constant to the solution

= \frac{x ^{10}}{10} + \frac{77 x ^{9}}{9} + \frac{657 x ^{8}}{2} + 7452 x^{7} + 110565 x^{6} + \frac{5603094 x ^{5}}{5} + 7853517 x^{4} + 37555164 x^{3} + \frac{234365481 x ^{2}}{2} + 215233605 x + C

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Frequently Asked Questions (FAQ)

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