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- ?Lv 56 years ago
sqrt(tan(x)) + sqrt(cot(x)) dx
= (sinx+cosx) /sqrt((sin2x) /2) dx
= (sinx+cosx) /sqrt( ( (cosx-sinx)^2-1)/2) dx ......just remember (cosx-sinx)^2=1-sin2x
now sub cosx-sinx=u..sinx+cosx dx=du
hernce
I=sqrt2 du/sqrt(u^2-1)
I=sqrt2 log| u+sqrt(u^2-1)| + C
now sub back...
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