Question

Integrate the following with respect to x.

x⁸(1 + x⁹)⁵ 

Answer 1

Let f(x) = 1 + x⁹

Then f'(x) = 9x⁸ 

So `int x^8 (1 + x^9)^5  "d"x = 1/9 int 9x^8(1 + x^9)^5  "d"x`

= `1/9 int ["f"(x)]^5 "f'"(x)  "d"x`

= `1/9 ["f"(x)]^6/6 + "c"`

= `1/54 (1 + x^9)^6 + "c"`