Question

Tolong dijawabnya pake intergal parsial pointnya kasi gede nih. nomer 14 ya thanks

Answer 1

Verified answer

InTegraL ParsiaL

Misal :
u = x --> du = dx

v = (x + 5)^1/2
dv = 1/2 (x + 5)^-1/2 dx
(x + 5)^-1/2 dx = 2 dv

∫ u dv = uv - ∫v du

▶
∫x/√(x + 5) dx
= ∫x (x + 5)^-1/2 dx
= ∫u . 2dv
= 2 (uv - ∫v du)
= 2 [x(x + 5)^1/2 - ∫(x + 5)^1/2 dx]
= 2 [x(x + 5)^1/2 - 1/(3/2) (x + 5)^3/2] + C
= 2 [x(x + 5)^1/2 - 2/3 (x + 5)^3/2] + C
= (2√(x + 5)) (x - 1/3 (x + 5)) + C
= (2√(x + 5)) (2/3 x - 5/3) + C
= (2/3)(√(x + 5)(2x - 5) + C