# Integrating Friedmann Equation of Multi-component universe respect to a and t

 P: 19 I am having a trouble finding relationship between 'a' and 't' by integrating friedmann equation in a multi-component universe. It would be very helpful if you can help me with just matter-curvature only universe and matter-lambda only universe. The two integrals looks like following. Matter-curvature only: $$H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1-Ω_0)]^{1/2}}$$ Matter-Lambda only: $$H_0 t = ∫_0^a \frac{da}{[Ω_0/a + (1-Ω_0)a^2]^{1/2}}$$ Thank you for your help.