Integrating,
Example4:
This examplerequiresus to use trigonometricidentitiesbeforewe substitute.Evaluate
Solution:
Since , the integralbecomes
Substitutingfor the argumentof the secant, then or Thusour integral
becomes,
Someintegrationsof trigonometricfunctionsinvolvethe logarithmicfunctionsas a solution,as shownin the
followingexample.
Example5:
Evaluate.
Solution:
As you may haveguessed,this is not a straightforwardintegration.We needto makeuse of trigonometric
identitiesto simplifyit. Since