Question

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Q. Solve Integral tanx dx .. limit 0 to pie/2 .

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Answer 1

tan(x) = sin(x)/cos(x) 

u = cos(x) 
du = -sin(x) dx, -du = sin(x) dx 

your new integral is: 

-Sdu/u = -ln |u| 

-ln|cos(x) | 

evaluating from 0 to pi/2 

[(-ln|cos(pi/2) | ] - [-ln|cos(0)|] 

One problem, cos(pi/2) = 0, hence ln|cos(pi/2) | is undefined

Answer 2

The given integral solutions diverges.

So, therefore the integral is undefined.

Hope this helps!