Question

2integration sin2x tan2x dx​

Answer 1

Answer:

sin(2x)tan(2x)dx=12∫sin2(2x)1−sin2(2x)cos(2x)d(2x)

Make the substitution sin(2x)=t⟹cos(2x)d(2x)=dt . Thus,

∫sin2(2x)1−sin2(2x)cos(2x)d(2x)=t21−t2dt

=∫11−t2dt−∫dt=12ln∣∣∣1+t1−t∣∣∣−t+c