Integration of (1+tanx)/(1-tanx) ...?

[Lois.Cypher]

∫(1+tanx)/(1-tanx) the answer is supposed to be -log| cosx - sinx | + C, but I just can't seem to get there. Can someone please tell me the steps to get there?

[ajb]

What have you got so far?

 

One hint is to simplify [math]\frac{1+ \tan(x)}{1-\tan(x)}[/math] by multiplying and dividing by [math]\cos(x)[/math]. Do this and then see if you notice anything about the numerator and the denominator.

Edited August 14, 2012 by ajb

[Lois.Cypher]

@ajb

 

Ahh thanks a lot, I understand now.

[ajb]

Ahh thanks a lot, I understand now.

 

Great.

 

I am glad to have helped.

[abvegto]

take tanx = sinx / cosx ...then simplify then rationalize