Please show how to integrate! ?

Question

20

___x______

sqrt(9+2x) dx

0

Answer 1

∫ [20x / sqrt(9 + 2x)] dx

Let u = sqrt(9 + 2x)

u^2 = 9 + 2x

2u du = 2 dx

dx = u du

Also, u^2 = 9 + 2x implies x = (u^2 - 9)/2

Plugging in gives :

∫ {[20(u^2 - 9)/2]/u} * u du

= ∫ 10(u^2 - 9) du

= ∫ (10u^2 - 90) du

= 10u^3/3 - 90u + C

Substituting :

= 10(9 + 2x)sqrt(9 + 2x)/3 - 90sqrt(9 + 2x) + C

= (20/3)(x - 9)sqrt(9 + 2x) + C