Question

求过程！！！万分感谢

Answer 1

∫(0->π/2) (x+sinx)/(1+cosx) dx
=∫(0->π/2) x/(1+cosx) dx +∫(0->π/2) sinx/(1+cosx) dx
=∫(0->π/2) x/(1+cosx) dx -[ln|1+cosx|]|(0->π/2)
=∫(0->π/2) x/(1+cosx) dx +ln2
=∫(0->π/2) x/(2[cos(x/2)]^2) dx +ln2
=(1/2)∫(0->π/2) x[sec(x/2)]^2 dx +ln2
=[ ∫(0->π/2) xdtan(x/2) ]+ln2
= [xtan(x/2)]|(0->π/2) -∫(0->π/2) tan(x/2) dx + ln2
=π/2 - 2[ ln|cos(x/2)|] (0->π/2) + ln2
=π/2 - 2( -(1/2)ln2 ) + ln2
=π/2 + 2ln2