Question

help with understanding steps in integrating (9x^2 - 12x +4)^-1

Answer 1

I know the answer is 1/(6 - 9x) but the question I have has to do with:

For the integrand 1/(3 x-2)^2, substitute u = 3 x-2 and du = 3 dx:
= 1/3 integral 1/u^2 du

Answer 2

still need help?

Answer 3

Yep, please

Answer 4

specifically: why du = 3 dx?

Answer 5

Let u = 3x -2 --> du = 3 dx
This step means you take derivative of u with respect to x, the left hand side is \(\dfrac{du}{dx}\)

Answer 6

the right hand side is 3.

Answer 7

so that du = 3 dx

Answer 8

Alright, I get that thanks! But then shouldn't the integral be S 3/u^2 rather than 1/3 S 1/u^2?

Answer 9

hey,\(\dfrac {du}{dx} = 3 \rightarrow \dfrac{du}{3}= dx\) , right? in original problem, you have dx only, not 3 dx, so that you must get dx only to replace to it, right?

Answer 10

Ahhh that makes a ton of sense! Thanks a lot!

Answer 11

:)

Answer 12

Do you have to use that reasoning everytime you use u substitution?

Answer 13

That is logic! not reasoning. When making some argument, you must follow the logic to know where you get the expression.

Answer 14

Okay thanks!

Answer 15

:)