Question

How do integrate x(6x-1)^2 without expanding

Answer 1

tried integration by parts?

Answer 2

I think it pays to expand it

Answer 3

expand and distribute the x

Answer 4

by parts

Answer 5

you could do it by parts, but why put yourself through all that doing the u and dv subs, it is straight forward integration by expanding it, and if you can do integrating by parts, you should be able to unfold that square and what not. All the other stuff is just pain for no reason. Not that by parts is so terrible just not necessary in this case.

Answer 6

∫x(6x-1)² dx
u = 6x -1 --> du/ 6 = dx
x = (u + 1)/6
= 1/36 ∫ (u + 1) u² du
= 1/36 ∫ (u³ + u² ) du
= (1/36 ) u^4/4 + u³/3
= (1/36 ) (6x-1)^4/ 4 + (6x-1)³/3 + C

Answer 7

= (1/36 ) (6x-1)³ [ (6x-1)/4 + 1/3 ]
= (1/36 ) (6x-1)³ (18x + 1)/ 12
= = (1/432 ) (6x-1)³ ( 18x +1)