I have problems with integrating this

[mitochondria]

I have problems with integrating this... :(

$$\int_{0}^{x}\frac{1}{\sqrt{a^2 - b/x}}dx$$

I have tried substituting 1/x with u and so on... But it doesn't seem to work :(

Thanks in advance!

 

[acm]

1/Sqrt(a^2 - b/x)
1/sqrt(a^2x - b)/Sqrt(x)
Sqrt(x)/ Sqrt(a^2x - b)
Let u = a^2x - b
du/dx = a^2
du/a^2 = dx
u+b/a^2 = x
Integral becomes - (1/a)Sqrt(u+b) * 1/Sqrt(u) * du/a^2
1/a^3 + 1/a^3sqrt(b/a) du

 

[mitochondria]

Thank you :)

(By the way, I think you meant 1/a^3[sqrt((u+b)/u)] for the last part, right?)