Integrating c1*x^c2*ln[-1+sqrt(1+c3*x^c4)]

[natlight]

Hi,

Can anyone suggest how to integrate the following function, in which all the c's are constants:

c1 * x^c2 * ln [ -1 + sqrt (1 + c3 * x^c4) ]

Much obliged!

 

[e2e8]

Well, Mathematica yields:

-(1/(2 (1 + c2)^2))
c1 x^(1 +
c2) (c4 +
c4 Hypergeometric2F1[1/2, (1 + c2)/c4, (1 + c2 + c4)/
c4, -c3 x^c4] - 2 (1 + c2) Log[-1 + Sqrt[1 + c3 x^c4]])

I am not familiar with the Hypergeometric2F1 function.