the integral of xtanx dx

Question

integral of xtanx dx

Answer 1

Apply formula: .

let u = x, v = tan x, , .

Apply formula:

.

Comments

That solution you have given is wrong.. You cant just plug in (-ln|cosx|) into that formula as (x) and (-ln|cosx|) are two completely different functions.

For example, as integral xdx= (x^2)/2 + C, we cant say that integral of tanxdx is just (tan^2x)/2 + C. Which is what youre implying. 

 If you do want to continue along those lines, you have to use substitution first, but in this case, that method wont work.

In reply to your question, you cannot evaluate such an integral, at least you cant pinpoint a particular value unless you have limits. Hope the folllowing link answers your query..

http://mathforum.org/library/drmath/view/53561.html

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