Lets say the denominator = x to save me from typing alot.
∫ -1/x
∫ -1/2 * 2/x
since -1/2 is a constant you may bring it to the front.
-1/2 ∫ 2/x
See how they are the same?
This problem has been worked out for me, but I am confused about what exactly is going on in it.
Problem: Find the indefinite integral.
∫-1/sqrt(1-(2t-1)^2) dt
Step 1: Let u= 2t -1
Step 2: du= 2 dt
Step 3: ∫ -1/sqrt(1-(2t-1)^2) dt
= -1/2 ∫ 2/sqrt(1-(2t-1)^2) dt
Step 4: = -1/2 arcsin(2t-1) + C
The main thing I don't understand is where the
-1/2 before the ∫ sign is coming from in Step 3, and why the -1 changed to a 2 in the part after the ∫ sign. If anyone could explain to me what is going on in this problem I would greatly appreciate it. Thanks.