How do you integrate #int dx/(x^2+25)# using trig substitutions?
Use the identity
Reverse the substitution; substitute
Please see below.
A good way to sort out trig substitutions is to recall the pythagorean identities in trig.
In this case, we have a square plus a number. We think about how to use
Eventually (perhaps by going through the list of pythagorean identities) we recall that
We want to have
We also get
# = 1/5 int d theta = 1/5 theta + C#