Question

How do I solve "integral [ x * (3-x)^7 ] dx" ?

Answer 1

we will use product rule
let $ represent integral
$uv dx = u $v dx - $ (du/dx $v dx) dx
$x*(3-x)^7 dx = x $(3-x)^7 dx - $dx/dx $ (3-x)^7 dx
= -x/8 (3-x)^8 +1/8$(3-x)^8 dx
= -x/8 (3-x)^8 -1/72 (3-x)^9 +c

Answer 2

i was trying to solve it by using substitution. so i substituted z=3-x ... could you tell me how it works from there?

Answer 3

dont use substitution u'll again get something like 3-z in place of x.