take t=e^{secx^2} 

then differentiate it,

dt=e^{secx^2}.secx².tanx².2x.dx

dt/2=e^{secx^2}secx²tanx².x.dx

in the integration part,(ie) in your question

the Nr can be written as,

=(x tanx² e^{secx^2}/cosx² ) dx

=x secx² tanx² e^{secx^2}dx

=dt/2

after removing the integration symbol,(ie) after doing integration

it will become 

=t/2

=e^{secx^2}/2

this is the answer