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∫(sinx+cosx)/(sinx-cosx) dx
=∫(sinx+cosx)^2/州渗袭喊信[(sinx)^2-(cosx)^2] dx
=-∫ (1+ sin2x)/cos2x dx
=-∫ ( sec2x + tan2x) dx
= - [(1/2)ln|sec2x+ tan2x| - (1/2)ln|cos2x| ) + C
=(1/册兄2)ln |cos2x/(sec2x+tan2x)| + C
∫√ [(1+x)/(1-x)] dx
=∫ [(1+x)/√(1-x^2)] dx
let
x= siny
dx = cosy dy
∫ [(1+x)/√(1-x^2)] dx
=∫ (1+siny) dy
= y - cosy + C
= arcsinx -√(1-x^2) + C
=∫(sinx+cosx)^2/州渗袭喊信[(sinx)^2-(cosx)^2] dx
=-∫ (1+ sin2x)/cos2x dx
=-∫ ( sec2x + tan2x) dx
= - [(1/2)ln|sec2x+ tan2x| - (1/2)ln|cos2x| ) + C
=(1/册兄2)ln |cos2x/(sec2x+tan2x)| + C
∫√ [(1+x)/(1-x)] dx
=∫ [(1+x)/√(1-x^2)] dx
let
x= siny
dx = cosy dy
∫ [(1+x)/√(1-x^2)] dx
=∫ (1+siny) dy
= y - cosy + C
= arcsinx -√(1-x^2) + C
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