now use the substitution for the last integral
Hi the question is evaluate the integral
integral sign (S) cos^-1 (2x) dx using integration by parts
SO I let t = 2x so dt = 2 dx so dx= dt/2
So the original equation becomes S cos^-1 t (dt/2)
Then I let u = cos^-1 t so du = -dt/(1-t^2))^(1/2)
then dv = dt so v = t
So the original equation is now (1/2) S cos^-1 t dt
= (1/2) ((u cos^-1 u ) - S u (-du/sqrt(1-u^2)))
= (1/2) (u cos-1u - (1/2)u^2 (-du/sqrt (1-u^2)))
Is there any way to simplify this further or do I just substitute 2x and 2 dx back into the equation?
Thanks
Calculus beginner