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tanx.sec2x.dx=
integral tanx.sec2x dx=integral sinx/(cosx.cos2x) dx=integral sinx/cosx(2cos^2x-1) dxput cosx =ton diff. w.r. to x-sinx dx=dt=>integral (-dt)/t(2t^2-1)Using Partial fraction we getintegral (1/t -1/root2(t.root2.-1) -1/root2.(troot2+1))=logt-1/2loh(troot2-1)-1/2 .log(troot2+1)=log cosx-1/2log(2cos^2x-1)=logcosx -1/2 logcos2x=log (cosx/ root of cos2x)Thanks & RegardsRinkoo GuptaAskIITians Faculty
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