integral 5x (1-x)^6dx

misalkan 1 - x = u
dx -1 = du
dx = -du
1 - x = u
- x = -1 + u
x = 1 - u
rubah soal ke bentuk u
5x(1 - x)^6 dx
= 5(1 - u) u^6 -du
= -5(1 - u) u^6 du
= (-5 + 5u)u^6 du
= (-5u^6 + 5u^7 ) du
= (5u^7 - 5u^6) du
baru diintegralkan
= (5 / 7+1)u^8 - (5 / 6+1)u^7 + C
= (5/8)u^8 - (5/7)u^7 + C
= (5/56)u^7 (7u - 8) + C
kembalikan u = 1 - x
= (5/56)(1 - x)^7 (7(1 - x) - 8) + C
= (5/56) (1 - x)^7 (7 - 7x - 8) + C
= (5/56) (1 - x)^7 (-7x - 1) + C