Question

两题不定积分∫x(secx^2)tanx dx∫x^(1/2)lnx dx

Answer 1

∫x(secx^2)tanx dx =∫xtanxdtanx=x(tanx)^2-∫tanxdxtanx=x(tanx)^2-∫[(tanx)^2+xtanx(secx)^2]dx=x(tanx)^2-∫[(secx)^2-1]dx-∫x(secx)^2tanxdx=x(tanx)^2-tanx+x-∫x(secx)^2tanxdx所以∫x(secx^2)tanx dx =(1...