MIND FREK INTEGRAL(2)

write sin2x as

( sinx + cosx ) ^2 = 1 + sin2x

sin2x = ( sinx + cosx ) ^2 - 1

\int \frac{cosx - sinx }{\sqrt{8 - [ ( sinx + cosx ) ^2 -1 )] }}

\int \frac{cosx - sinx }{\sqrt{9 - ( sinx + cosx ) ^2 }}

put sinx + cosx = t

cosx - sinx dx = dt

\int \frac{dt }{\sqrt{9 - ( t ) ^2 }} \rightarrow \sin^{-1}\left( \frac{t}{3}\right)

got it simple it was.i had not tried it.[4][4]