How do I integrate these 3 functions?

[Odyssey]

How do I integrate these 3 functions?

(1) $$\alpha(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{a^ 2-u^2}}$$

(2) $$\beta(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{u^ 2+b}}$$

(3) $$\beta(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{u^ 2-b}}$$

A million thanks in advance.

 

[vsage]

Ouch I saw a previous post like this. It's nothing but trig substitution..
http://www.mathwords.com/t/trig_substitution.htm

 

[Odyssey]

thank you very much. Let me try to work this through.

 

[vsage]

thank you very much. Let me try to work this through.

Sorry =X hint deleted.

 

[Motifs]

The first one can be solved by letting u=asint
The second and the third is with u=sqrt(b).sint/cost
The rest is left for you, honey!

 

[Motifs]

Sorry =X hint deleted.

What is X hint ?

 

[Odyssey]

The first one can be solved by letting u=asint
The second and the third is with u=sqrt(b).sint/cost
The rest is left for you, honey!

Thank you very much!

 

[vsage]

What is X hint ?

I was doing a muting of myself emoticon for nearly the same text you just put up :) Oh well.