计算下列定积分 11:e^2xcosxdx 14:cos(inx)dx（第11题和第14题）

(11)
∫(0->π/2) e^(2x). cosx dx =∫(0->π/2) e^(2x). dsinx
= [e^(2x). sinx ]|(0->π/2) - 2∫(0->π/2) e^(2x). sinx dx
=e^π +2∫(0->π/2) e^(2x). dcosx
=e^π +2[e^(2x).cosx]|(0->π/2) -4∫(0->π/2) e^(2x). cosxdx
5∫(0->π/2) e^(2x). cosx dx =e^π -2
∫(0->π/2) e^(2x). cosx dx =(1/5)(e^π-2)

(14)
∫(1->π/2) cos(lnx)dx=[xcos(lnx)](1->π/2) +∫(1->π/2) sin(lnx)dx
=(π/2)cos(ln(π/2))-1 +[xsinlnx](1->π/2) -∫(1->π/2) cos(lnx)dx
2∫(1->π/2) cos(lnx)dx =(π/2)cos(ln(π/2))-1 +(π/2)sinln(π/2)
∫(1->π/2) cos(lnx)dx =(1/2) [ (π/2)cos(ln(π/2))-1 +(π/2)sinln(π/2) ]