Integral x kuadrat akar 1-x dx

int x√(x+1) dx
misal, u = x + 1  --------> x = u - 1
du = dx
shg, integral di atas dapat menjadi :
int (u-1) √u  du
= int (u - 1) u^(1/2)  du
= int (u^(3/2) - u^1/2)  du
= 2/5 u^(5/2) - 2/3 u^(3/2) + C
= 2/5 (x+1)^(5/2)  -  2/3 (x+1)^(3/2) + C

InTegraL
>> Parsial

turunan.....integral
x² .............. (1 - x)^1/2
2x ............. -2/3 (1 - x)^3/2
2 ............... 4/15 (1 - x)^5/2
0 ............... -8/105 (1 - x)^7/2

∫x² √(1 - x) dx
= x²(-2/3 (1 - x)^3/2) - 2x(4/15 (1 - x)^5/2) + 2(-8/105 (1 - x)^7/2) + C
= -2/3 x² (1 - x)^3/2 - 8/15 x(1 - x)^5/2 - 16/105 (1 - x)^7/2 + C