3+(sinx)^2分之一的不定积分

Question

3+(sinx)^2分之一的不定积分

Answer 1

∫ 1/[3+(sinx)^2] dx
=∫ (secx)^2/[3(secx)^2+1] dx
=∫ 1/[3(secx)^2+1] dtanx
=∫ 1/[3(tanx)^2+4] dtanx
= 1/(2√3)∫ 1/[(√3/2tanx)^2+1] d(√3/2tanx)
= 1/(2√3) arctan(√3/2tanx) + C