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e-lub [12.9K]
3 years ago
6

The integral of x(6x+7)^8

Mathematics
1 answer:
prisoha [69]3 years ago
8 0
Hello,

Let's assume t=6x+7
x=(t-7)/6
dt=6dx

\int\limits{x(6x+7)^8} \, dx = \int\limits { \dfrac{t-7}{6} t^8} \, \dfrac{dt}{6} \\

= \dfrac{1}{36}  \int\limits{ (t^{9}-7t^8) \, dt = \dfrac{1}{36} ( \dfrac{t^{10}}{10}- \dfrac{7t^9}{9} )+C\\

=  \dfrac{(6x+7)^9*(54x-7)}{3240} +C

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