How do you integrate #int 1/(xsqrt(25-x^2))# by trigonometric substitution?
Rearrange. Substitute. Voila!
Then we set:
Our integral with the variable t now reads:
Whence we rearrange and get:
And this integral is solved in the following way:
We make a small but cunning rearrangement, namely:
So that our integral now reads :
Why this? Because if we now set
Which is just :
The one half comes about from the partial fraction decomposition. This is just :
However this is a solution expressed through the variable u, but back substitution is done trivially if needed.
Let us subst.