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Problem with integrating the expression of M

Hi. I have the following code that I want to integrate and differentiate, but I am stuck at the expression of M, where it is unable to integrate. Is my coding wrong?

c,t = var('c t')
Pi = RR.pi()
M=integrate(1/(sqrt(1-t^2)*(t-c)),t,-0.9,0.9);M #cannot seem to integrate this wrt to t
I=(c^2-1)*(L+(1-c^2)*M);I #equation I that involves M
P=I.diff(c);P #differentiate I wrt to c to obtain equation P

I have tried integrating M by hand which gives me a closed-form involving log function, but I can't seem to integrate it here using Sage.