Integration of ln(1 + cosX)

given from lower limit 0 to upper limit pie

ln(1+cosX)=ln(2.cos^2 X/2)=ln2 + 2lncos X/2
now integrate the func..
for ln2...integral=xln2
for 2ln cos X/2 aplly u.v formula by taking 2=v,ln cos X/2=u
and then apply limits.