Solution of Friedmann equation w/ Cosmological Constant

[nicksauce]

Homework Statement

Solve for the age of the universe as a function of scale factor in a cosmology with $\Omega_{M}=0.3$, $\Omega_{\Lambda}$=0.7.

Homework Equations

The Attempt at a Solution

$$(\frac{\dot{a}}{a})^2=H_0^2(0.3a^{-3}+0.7)$$

$$\frac{da}{a\sqrt{0.3a^{-3}+0.7}}=H_0dt$$

At this point, Maple seems unable to do this integral, and I am stuck. Any tips?Errr... Nevermind, I got it to work eventually.

 

[CompuChip]

Errr... Nevermind, I got it to work eventually.

Would you mind sharing? Some people may find it useful!