Basic Integration help

[armen]

Hi there

I'm trying to understand integration as I just started but I can't recall a part of my teacher's explanation.

I have to integrate this:

. . . . .\(\displaystyle \displaystyle{ \int\, \frac{5}{2\, -\, 6x}\, dx }\)

In my notes it shows that

\(\displaystyle =\, 5\, \displaystyle{ \int\, \frac{1}{2\, -\, 6x}\, dx }\)

\(\displaystyle =\, \dfrac{5\, \ln\, |\, 2\, -\, 6x\, |\, }{-6}\, +\, c\)

Which is understand somewhat.

I don't understand why the final answer has -6 at the bottom.

 

[Deleted member 4993]

Hi there

I'm trying to understand integration as I just started but I can't recall a part of my teacher's explanation.

I have to integrate this:

. . . . .\(\displaystyle \displaystyle{ \int\, \frac{5}{2\, -\, 6x}\, dx }\)

In my notes it shows that

\(\displaystyle =\, 5\, \displaystyle{ \int\, \frac{1}{2\, -\, 6x}\, dx }\)

\(\displaystyle =\, \dfrac{5\, \ln\, |\, 2\, -\, 6x\, |\, }{-6}\, +\, c\)

Which is understand somewhat.

I don't understand why the final answer has -6 at the bottom.

substitute:

u = 2 - 6x

du = - 6 dx

dx = du/(-6)