Jawabanmu

2014-07-16T07:48:36+07:00
#1
Anggap:
u = x² + 2x - 1
<> du = (2x + 2) dx
<> du/2 = (x + 1) dx
∫ (x + 1) √(x² + 2x - 1) dx
= ∫ √u du/2
= 1/2 . 2/3 u√u + c
= 1/3 u√u + c
= 1/3 (x² + 2x - 1)√(x² + 2x - 1) + c

#2
Anggap:
u = 1 - 2x
<> du = -2 dx
<> -du/2 = dx
∫ sin² (1 - 2x) dx
= -1/2 ∫ sin² u du
= -1/2 ∫ sin² u du
= -1/4 ∫ (1 - cos 2u) du
= -1/4 (u - 1/2 sin 2u) + c
= -u/4 + 1/8 sin 2u + c
= (2x - 1)/4 + 1/8 sin (2 - 4x) + c

#3
∫ (sin x + cos x)² dx
= ∫ (sin² x + cos² x + sin 2x) dx
= ∫ (1 + sin 2x) dx
= x - 1/2 cos 2x + c