since
so that
Example2:
Evaluate.
Solution:
Again,we wantto first to eliminatethe radical.Consultthe tableaboveand substitute. Then
. Substitutingbackinto the integral,
Usingthe integralidentityfrom the sectionon TrigonometricIntegrals,
and letting we obtain
Lookingat the trianglesabove,the third trianglerepresentsour case,with. So
and thus , whichgives\tan. Substituting,