Question

求解不定积分x/(1+sinx)

Answer 1

简单计算一下即可，答案如图所示

Answer 2

∫x/(1+sinx)*(1-sinx)/(1-sinx) dx
=∫(x-xsinx)/cos^2x dx
=∫xsec^2x dx-∫xsecxtanx dx
=∫x d(tanx)-∫x d(secx)
=xtanx-∫tanx dx-(xsecx-∫secx dx)
=xtanx-sec^2x-xsecx+ln(secx+tanx)+C