Integral dari [tex]x \sqrt{x + 1} \: dx[/tex]

jawab

∫ x √( x+1) dx

parsial

def...........int
x..............(x +1)^(1/2)
1..............2/3 ( x+ 1)^(3/2)
0..............2/3 (2/5) (x +1)^(5/2)

= 2/3 x (x +1)^(3/2) - 4/15 (x + 1)^(5/2)

= 2/15 (x + 1)^(3/2)  [ 5x - 2 (x +1)]
= 2/15 (x + 1)^(3/2) [ 3x - 2 ]

= 2/15 (3x - 2) (x +1)√ (x + 1) + c