Question Number 10188 by ridwan balatif last updated on 29/Jan/17

Commented byridwan balatif last updated on 29/Jan/17

∫(√(1−tan^2 2x+tan^4 2x−tan^6 2x+...))dx=...? 1−tan^2 2x+tan^4 2x−tan^6 2x+...= U_1 =1 r=−tan^2 2x S_∞ =(U_1 /(1−r))=(1/(1+tan^2 2x))=(1/(sec^2 2x))=cos^2 2x S_∞ =cos^2 2x (√(1−tan^2 2x+tan^4 2x−tan^6 2x+...))=(√(cos^2 2x))=cos2x so, ∫cos2x dx=(1/2)sin2x + C is it true my way?