Question

Integral kelas XII? Bantu ya plss

Integral dari (tan 2x + sec 2x)^2

Tlong disertakan cara ya mksh ^^

Answer 1

∫ (tan 2x + sec 2x)² dx =
u = 2x --> du = 2 dx ---> dx = 1/2 du
=  ∫ 1/2 (tan u + sec u)² du
= ∫ 1/2 (tan² u + 2 tan u sec u+ sec² u) du
= 1/2 (tan u - u  + 2 sec u + tan u ) + c
= 1/2 ( 2 tan u + 2 sec u - u) + c
=  tan u + sec u - 1/2 u + c
= sin 2x/cos 2x + 1/cos 2x - 1/2 (2x) + c
= (sin 2x +1)/cos 2x - x + c
= (2 sin x cos x + sin² x + cos² x) / (cos x +sin x)(cos x - sin x)  - x + c
= (sin x + cos x)(sin x + cos x)/ (cos x +sin x )(cos x - sin x ) - x + c
= (sin x + cos x)/(cos x - sin x) - x + c