Integral - Exercises on sum decomposition

• 3 exercises on the integration to sum decomposition.

 Exercises I

 

 Adding and subtracting 1 to the numerator of the integrated function we get :

Exercises II

Calculate the indefinite integral

Reminding the definition of the tangent function, we get :

For sum decomposition we get :

Exercises III

Calculate the indefinite integral

Reminding  the formula for duplication

 

which implies that

We get : 

In the last step has been taken that D(sen2x) = 2cos2x.