∫cos( x^5) dx ?

Answer 1

I = ∫ cos x (cosx)^4 dx
I = ∫ cos x (1 - sin ² x) (1 - sin ² x) dx
Let u = sin x
du = cos x dx
I = ∫ (1 - u ²)(1 - u ²) du
I = ∫ (1 - 2 u ² + u^4) du
I = u - (2/3) u³ + u^5/5 + C
I = sin x - (2/3) sin ³ x + (sin^5x) / 5 + C

Answer 2

Have you tried with partial integration? F.e.: u=cos xˇ5 , dv=dx