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what is integration of tanX?

Mathematics
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what is integration of tanX?

Dec 20th, 2014

∫ tan(x) dx = ∫ sin(x)/cos(x) dx = 
Let cos(x) = u 
-sin(x) dx = du 
sin(x) dx = -du 
The integral becomes 

- ∫ du/u = -ln|u| = - ln |cos(x)| + C 

You do not have a negative sign in your answer.

OR 

    ∫Tan(x)dx=∫sin (x)/cos(x) dx 

    Let cos (x)=u => du=-sin(x)dx so the integral becomes -∫du/u=-ln u and u must be >0. So you write -ln|u|. 
    Substitute back and get -ln|cosx| and you were off by a sign.

Dec 20th, 2014

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