Question

Evaluate the following integral using substitution rule, `int x(2x+5)^8 dx` Online i saw people solving for x too, i dont get that part?

Answer 1

`1/360(2x+5)^9(18x-5)+C`

Explanation:

Let `2x+5=t`, so that

`dx=1/2dt and x = 1/2(t-5)`. The integral becomes

`int1/2(t-5)t^8 1/2dt`

`=1/4(t^10/10-5t^9/9)+C`

`=1/360(2x+5)^9(9(2x+5)-50)+C`

`=1/360(2x+5)^9(18x-5)+C`