Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Please show me the steps of the following integration. I got an answer in Wolfram, but I need steps..

$$\int \frac{\mathrm dx}{\sqrt[3]{\tan\,x}}$$

share|improve this question
    
@draks here it is. And WA do not know closed form for this integral –  Norbert Jul 31 '12 at 11:02
    
Well, I'm sorry its not arctan, its just tan –  Anubis Jul 31 '12 at 11:05
    
This is the link –  Anubis Jul 31 '12 at 11:08
    
@draks sorry, I've typed it wrong. It's now corrected. Can you evaluate now? –  Anubis Jul 31 '12 at 11:10
    
Aha, so please edit your question accordingly!!! and click on "show steps" in your linked W|A page... –  draks ... Jul 31 '12 at 11:10

1 Answer 1

up vote 8 down vote accepted

We try the substitution $t^3 = \tan^2 x$. Therefore, $3t^2 dt = 2 \tan x \sec^2 x dx$, giving us $\frac{dx}{\sqrt{t}} = \frac{3 dt}{2(1+t^3)}$.

Thus, we will only evaluate $\int \frac{3 dt}{1+t^3} $, divide by $2$ and substitute back. Note that $3 = (1-t+t^2) + (2-t)(1+t)$, reducing our integral to $$ \int \frac{dt}{1+t} + \int \frac{(2-t)dt}{1-t + t^2} $$ I won't elaborate further, since our integrals are already in standard forms.

share|improve this answer
    
Wow..a cleaver approach. You are a genius..! –  Anubis Aug 1 '12 at 9:23

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.