Question

Kuis renyah dapet poin :p

∫ (x³ dx) / √(3 + x²)

hayuuu :D

Answer 1

∫ (x³ dx) / √(3 + x²)
misalkan:
u = 3 + x²
du = 2x dx
∫ (x³ dx) / √(3 + x²)
= ∫ (x² . x dx) / √(3 + x²)
= 1/2 ∫ (u - 3) . du) / √u
= 1/2 ∫ (u - 3) / √u du
= 1/2 ∫ √u - 3/√u du
= 1/2 [ 2/3 u√u - 6√u] + c
= 1/3 u√u - 3√u + c
= 1/3 √u[u - 9] + c
= 1/3 √(3 + x²) [3 + x² - 9] + c
= 1/3 √(3 + x²) [x² - 6] + c