求下列不定积分：∫[sinx/(1+sinx)]dx
∫[six/(1+sinx)]dx=∫[sinx(1-sinx)/(1+sinx)(1-sinx)]dx=∫(sinx/cos2x)dx-∫tan∫2xdx=∫d(cosx)/cos2x-∫(1/cos2x-1)dx=1/cosx-tanx+x+c．
求下列不定积分：∫[sinx/(1+sinx)]dx
∫[six/(1+sinx)]dx=∫[sinx(1-sinx)/(1+sinx)(1-sinx)]dx=∫(sinx/cos2x)dx-∫tan∫2xdx=∫d(cosx)/cos2x-∫(1/cos2x-1)dx=1/cosx-tanx+x+c．
