Solving an integral, what to substitute

[beta3]

Hi

Recently I found an integral which I can't solve, I don't know or can't guess how and what to substitute.

$$\int_{\frac{3}{2}}^{2}(\frac{x-1}{3-2})^{\frac{1}{2}}dx$$


Please tell me what you would substitute and why you would do that
Thanks


ps:
the solution isn't important to me, i want to understand and see how one can do that by oneself

 

[Hurkyl]

I would start with the substitution 3 - 2 = 1.

This is really an easy problem if you think about it at all -- think of an integral that you can do that looks similar, and make a substitution that makes this integral look more like that integral.

 

[beta3]

oh, I actually noticed, that I made a typo, the denominator is wrong

here is the right one:
$$\int_{\frac{3}{2}}^{2}(\frac{x-1}{3-x})^{\frac{1}{2}}dx$$

still recomending the same substitution?

 

[Hurkyl]

The two substitutions that came to mind would still be two of the first things I'd try... I suspect still that both will work.

 

[arildno]

Arguably, the simplest substitution is to let the new variable equal the integrand.