Hey guys I cant solve one integral ∫1/√(1+cosx) dx I have started like ∫1/√(1+(cos^2 x/2 -sin^2 x/2)) dx = ∫1/√(cos^2 x/2 + cos^2 x/2) dx = ∫1/√(2cos^2 x/2) dx = 1/√2 ∫1/(cos x/2) dx = { substitution t= x/2 dx= 2dt } = 2/√2 ∫ 1/cost dt= 2/√2 ∫1/ ( cos^2 t/2 - sin^2 t/2) dt = 2/√2 ∫1/(cos^2 t/2 (1-(sin^2 t/2 /cos^2 t/2))) dt = 2/√2 ∫ 1/ cos^2 t/2(1-tg^2 t/2)) dt = { substitution t/2=u dt=2du} = 4/√2 ∫1/ cos^2u(1-tg^2 u) du = after this I dont know what to do can someone help me please.(adsbygoogle = window.adsbygoogle || []).push({});

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# Substitution in integral

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