Question

Hasil dari integral cos 2x√sin 2x dx

Answer 1

Verified answer

Integral TakTentu

∫ cos 2x  √ (sin 2x)  dx = 
∫  cos 2x . (sin 2x) ¹/²  dx

u = sin 2x
du = 2 cos 2x  dx
cos 2x  dx = 1/2 du

∫ cos 2x . (sin 2x)¹/²  dx =   1/2 ∫ u¹/² du
= 1/2 (2/3) (u)³/² + c
= 1/3 u√ u + c
= 1/2 sin 2x √ (sin 2x) + c

5) 
∫ (x² + 2) (x³ + 6x  + 1)¹/² dx
u = x³ + 6x + 1
du = 3x² + 6 dx
du = 3(x² + 2) dx
(x² + 2) dx = 1/3 du

1/3 ∫ u¹/²  du  =
= 1/3 (2/3) u³/² + c
= 2/9 u√u + c
= 2/9 (x³ + 6x +1) √(x³ +6x + 1) + c