(x+sinx)/(1+cosx)的积分
12个回答

∫((x+sinx)/(1+cosx))dx

=∫[(x+sinx)/2cos²(x/2)]dx

=∫(x+sinx)d(tan(x/2))

=(x+sinx)*tan(x/2)-∫tan(x/2)d(x+sinx)

=xtan(x/2)+sinx*tan(x/2)-∫tan(x/2)(1+cosx)dx

=xtan(x/2)+2sin(x/2)cos(x/2)*tan(x/2)-∫tan(x/2)*2cos²(x/2)dx

=xtan(x/2)+2sin²(x/2)-∫sin(x)dx

=xtan(x/2)+2sin²(x/2)-cos(x)+C

=xtan(x/2)+C1