trig integration troubles (1 Viewer)

[RideTheLightnin]

hey guys, stuggling with the algebraic rearrangement of some trig involved in integration

i dont understand how the last two steps work....
you have the theta - sintheta.costheta
and theta = sin^-1(x)^1/2
so you put that into theta - sintheta.costheta + c bit.....but i cant seem to do this algebracially to reach the final step

any help is GREATLY APPRECIATED
cheers

 

[Riviet]

It's just getting your answer in terms of the original variable in the question (being x).

From the substitution, x=sin²@

Then sin@=sqrt(x)

@=sin^-1{sqrt(x)}

Also, by drawing a right triangle, we find that cos@=sqrt(1-x)

Substitute these to get the final anwer.

 

[SoulSearcher]

sin(sin^-1sqrtx) = sqrtx
cos(sin^-1sqrtx) = sqrt(1-x)
Therefore sin(sin^-1sqrtx) * cos(sin^-1sqrtx) = sqrtx * sqrt(1-x)
= sqrt(x(1-x))