Question

Tentukan integral dari

1) ∫ (sin⁵ x²)(x cos x²)dx
2) ∫ (x² + 1)³ x . sin³ (x² + 1)⁴ cos (x² + 1)⁴ dx
3) ∫ (2x + 1) sin 3x dx

Answer 1

2)
misalkan u = (x²+1)⁴
du = 4 (x²+1)³ (2x) dx
du = 8 x(x²+1)³ dx
x(x²+1)³ dx = 1/8 du

∫(x²+1)³ x . sin³(x²+1)⁴  cos(x²+1)⁴ dx = 
= 1/8 ∫ sin³ u cos u du 
= 1/8 (1/4) sin⁴ u + c
= 1/32 sin⁴ (x²+1)⁴ + c

3) tabel parsial
2x + 1 .............sin 3x 
2................-1/3 cos 3x
0 ..............-1/9 sin 3x 

= - 1/3 (2x+1) cos 3x + 2/9 sin 3x + c