Hasil dari ʃ cos 2x √(sin⁡2x ) dx =….

Hasil dari ʃ cos 2x √(sin⁡2x ) dx =….

Jawaban Terkonfirmasi

$displaystyle intcos2xsqrt{sin2x},dx=intsqrt{sin2x}cdotcos2x,dx\\text{misal :}\sin2x=u\2cos2x,dx=du\\intsqrt{sin2x}cdotcos2x,dx=int u^frac12cdotfrac12,du\intsqrt{sin2x}cdotcos2x,dx=frac12int u^frac12,du\intsqrt{sin2x}cdotcos2x,dx=frac12cdotfrac1{frac12+1}u^{frac12+1}+C\intsqrt{sin2x}cdotcos2x,dx=frac12cdotfrac1{frac32}u^{frac32}+C\boxed{boxed{intsqrt{cos2xsin2x},dx=frac13sin2xsqrt{sin2x}+C}}$