integral × akar x-7 dx

InTegraL ParsiAl

u = x
dv = √(x - 7) dx ---> v = 2/3 (x - 7)^3/2

∫x √(x - 7) dx
= ∫u dv
= ∫x d(2/3 (x - 7)^3/2)
= 2/3 x(x - 7)^3/2 - 2/3 ∫(x - 7)^3/2 dx
= 2/3 x(x - 7)^3/2 - 2/3 . 2/5 . (x - 7)^5/2 + C
= (2/15)(x - 7)^(3/2) [5x - 2(x - 7)] + C
= (2/15)(x - 7)^(3/2) [3x + 14] + C