How do I integrate these 3 functions?

[Odyssey]

:confused: 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. :smile:

[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! :wink:

[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! :wink:

Thank you very much!! :tongue2:

[vsage]

What is X hint ????

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