One important question type to be able to answer is integrating squared trig functions. like cos^2(x)

This question requires selecting the correct double angle formulae.
cos(2x)=2cos^2(x)-1 is rearranged to 1/2(cos(2x)+1)
this can now be integrated with the students knowledge of standard integrals.
Cos integrates to sin and numbers integrate to x . Remembering the factor of 2 from the fact that its cos (2x) we get ;
1/4 (sin(2x)) +1/2 x