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1-2-1-cosh-t-dt-




Question Number 134812 by mohammad17 last updated on 07/Mar/21
∫(√((1/2)(1+cosh(t)))  dt
$$\int\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+{cosh}\left({t}\right)\right.}\:\:{dt} \\ $$
Answered by mathmax by abdo last updated on 07/Mar/21
I=∫(√((1+ch(t))/2))dt =∫(√(ch^2 ((t/2))))dt =∫ ch((t/2))dt  =2sh((t/2)) +C
$$\mathrm{I}=\int\sqrt{\frac{\mathrm{1}+\mathrm{ch}\left(\mathrm{t}\right)}{\mathrm{2}}}\mathrm{dt}\:=\int\sqrt{\mathrm{ch}^{\mathrm{2}} \left(\frac{\mathrm{t}}{\mathrm{2}}\right)}\mathrm{dt}\:=\int\:\mathrm{ch}\left(\frac{\mathrm{t}}{\mathrm{2}}\right)\mathrm{dt} \\ $$$$=\mathrm{2sh}\left(\frac{\mathrm{t}}{\mathrm{2}}\right)\:+\mathrm{C} \\ $$

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