hasil dari integral (x^2 + 2)(x^3 + 6x+1)^1/2 dx= lks 5 hal 13

Integral Substitusi.
Kelompok wajib kelas XI SMA kurikulum 2013 revisi 2016.

∫ (x² + 2)(x³ + 6x + 1)^(1/2) dx
= ∫ (x² + 2) √(x³ + 6x + 1) dx
u = x³ + 6x + 1
du / dx = 3x² + 6
= ∫ (x² + 1) √u du / (3x² + 6)
= 1/3 ∫ u^(1/2) du
= 1/3 [2/3 u^(3/2)] + C
= 2/9 (x³ + 6x + 1)^(3/2) + C
= 2/9 (x³ + 6x + 1) √(x³ + 6x + 1) + C