Question

∫ 4x/(2x-3)^3

Answer 1

\[\int \frac{4x}{(2x-3)^3}dx\]
u = 2x -3 => 2x = u + 2 => x = (u+2)/2
du / dx = 2

Answer 2

\[ \int \frac{ 2(u+2)}{u^3} * \frac{du}{2}\]

Answer 3

\[ = \frac{2}{2} \int \frac{u+2}{u^3}du\]

Answer 4

\[ \int \frac{u}{u^3}du + \frac{2}{u^3}du\]

Answer 5

\[ \int \frac{1}{u^2} du + 2 \int \frac{1}{u^3}du\]

Answer 6

You should be able to do it now.

Answer 7

May be there is a 3 that has dissapeared @Mimi_x3.

Answer 8

what 3?

Answer 9

In the step you wrote,
u = 2x -3 => 2x = u + 2 => x = (u+2)/2

Answer 10

oh pellet. consequences of not doing it on paper.

Answer 11

But I think, she/he can follow the steps. Very well done.

Answer 12

u = 2x - 3 => 2x = u + 3 => x = (u+3)/2
@AlanKYL: it's too long to type again, but i think you can still follow it. Just ping me, if you have any problems.