Integral dari x per √x+4 dx

Integral Substitusi.

∫ x / √(x + 4) dx
= ∫ (x + 4 - 4) dx / √(x + 4)
= ∫ [√(x + 4) - 4 / √(x + 4)] dx
u = x + 4
du / dx = 1
= ∫ [u^(1/2) - 4u^(-1/2)] du
= 2/3 u^(3/2) - 8u^(1/2) + C
= 2/3 (x + 4)√(x + 4) - 8√(x + 4) + C
= √(x + 4) [2/3 (x + 4) - 8] + C
= √(x + 4) (2/3 x - 16/3) + C
= 1/3 [2(x - 8) √(x + 4)] + C