How do you integrate #int 1/sqrt(-e^(2x) +9)dx# using trigonometric substitution?
Here is the corresponding right triangle from which you can extract all the parts for substitution:
You need to find the following and then systematically replace all x terms (rectangular) with
I'll start you off in the right direction:
We have then that:
Now differentiate with respect to
You can then rewrite that entire integrand in terms of
I'll give you one more piece and then I gotta sleep!
Well, referencing the triangle you can see that:
This says that:
You'll still need to find
So now you can systematically replace all rectangular terms with
That's your job!