Question

Hasil dari integral x akar x+1 adalah

Answer 1

Int  x√(x + 1) dx
misal, u = x + 1 -----> x = u - 1
du = dx
= int (u - 1)√u  du
= int (u - 1) u^(1/2)  du
= int u^(3/2) - u^(1/2)    du
= 1/(3/2 + 1) u^(3/2 + 1) - 1/(1/2 + 1)u^(1/2 + 1) + C
= 2/5 u^(5/2) -  2/3 u^(3/2) + C
= 2/5 (x+1)^(5/2) - 2/3 (x+1)^(3/2) + C