Expert: Steve Holleran - 12/2/2007

Question
use substituition to find the following integrals:

a) x ( x - 2 ) ^ 15
b) x ( 2 x + 1 ) ^ 1/2

Many thanks!

Answer
Hi again, Lill,

The first one I just finished for you.

On the second one, call u = 2x+1.  Then du = 2 dx, dx = 1/2 du,  and
x = 1/2 *(u-1).

So you have

 INT [ x(2x+1)^1/2 dx] = INT[1/2*(u-1) * u^1/2 * 1/2 du]

= 1/4 * INT [u^3/2 - u^1/2 * du]

= 1/4 * [(u^5/2) / (5/2) - (u^3/2) / (3/2)]

= 1/4 * [2/5 * u^5/2  - 5/2 * 2/3 * u^3/2]

= 1/10 * u^5/2 - 1/6 * u^3/2 + C

= 1/10 * (2x+1)^5/2 = 1/6 * (2x+1)^3/2+ C

Hope this is ok.

Steve