How do you integrate tanx?

Solution:

Integration is exactly the reverse process of differentiation. It is also known as antiderivative of a function.To integrate tanx we will express tanx in terms of sinx / cosx

∫ tanx dx = ∫ sinx/cosx.dx   

I = ∫ sinx/cosx.dx   ------------ (1)   

Assume u = cosx 

Thus, du = - sinx dx     

-du = sinx dx                 

Substituting u and du in the RHS of (1) we get,

I = ∫ (-1/u).du     

= - In |u| + C  [Since, ∫1/x.dx = In |x| + C] 

where, C is the constant of indefinite integration

On substituiting u = cosx  we will get,

= - ln |cosx + C|                               

Thus,  ∫ tanx dx = - ln |cosx + C| 

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How do you integrate tanx ?

Summary:

 ∫ tanx dx = - ln |cosx + c|