Hi there,

I was stumped on how to integrate the following with a suitable substitution

ò_1.5^2.5(4x²-9)^1/2 dx=a+bln(p),

stating your values of a, b, p.
Thanks for your help in advance.
Hal

The usual way is to either substitute x=(3/2)cosh u or x=(3/2)sec u. The standard textbook will tell you the former. I will do the latter:

x=3/2 sec u, dx=3/2 sec u tan u du

ò(4x²-9)^1/2 dx=ò9/2tan² usecu du=9/2òsec³ u-sec u du

Now recall that òsec u du=ln|sec u+tan u|+ constant and we have

òsec³ u du=tan u sec u-òtan² u sec u du=tan u sec u +òsec u du -òsec³ u du

so

òsec3 u du=

1 2

[tan u sec u +ln|sec u +tan u|]+

constant

Substitute and evaluate.

Kerwin

Hi Kerwin,

Thanks for those subs and the one with the Sec example.

Hal