Integration questions for my astoronomy class

[b_o3]

Hi, I have to do a lot of integration questions for my astoronomy class but I'm not really sure how to! for example how do u integrate from a number let's say a = 0, to a = 1/(1+z)... and dt = \frac{da}{H_0 \left(\frac{\Omega_{m,0}}{a} + a^2 \Omega_{\Lambda,0}\right)^{\frac{1}{2}}}

I've done a different kind of simple integration but i have no idea how this works,. thanks!

 

[Mentz114]

$$dt = \frac{da}{H_0 \left(\frac{\Omega_{m,0}}{a} + a^2 \Omega_{\Lambda,0}\right)^{\frac{1}{2}}}$$

Is this what you mean ?

 

[SGT]

To integrate $$\frac{du}{(a^2 + b^2 u^2)^{-\frac{1}{2}}}$$
make the variable change
$$\frac{bu}{a} = tan v$$
and remember that
$$1 + tan^2 v = sec^2 v$$

 

[b_o3]

yest mentz its that one