stuart clark Posted November 12, 2013 Share Posted November 12, 2013 Calculation of [math]\displaystyle \int\frac{1}{\left(1+x^4\right)^{\frac{1}{4}}}dx[/math] My Trial : [math]\displaystyle \int\frac{1}{x\cdot \left(x^{-4}+1\right)^{\frac{1}{4}}}dx[/math] Let [math]x^{-4}+1 = t^4[/math] and [math]\displaystyle \frac{1}{x^5}dx = -\frac{4t^3}{4}dt = -t^3dt[/math] [math]\displaystyle [/math] Now How can i solve after that Help please Thanks Link to comment Share on other sites More sharing options...

studiot Posted November 12, 2013 Share Posted November 12, 2013 (edited) Have you tried trigonometric substitution. with x = tan^{2}(t) and then use sec^{2}(p)= (1+tan^{2}(p)) Edited November 12, 2013 by studiot Link to comment Share on other sites More sharing options...

imatfaal Posted November 12, 2013 Share Posted November 12, 2013 Have you tried trigonometric substitution. with x = tan^{2}(t) and then use sec^{2}(p)= (1+tan^{2}(p)) Not sure I understand your substitution - that would give you tan(t) to the 8th power; shouldn't it be x^2=tan(t) to give denominator as (1+tan^2)^1/4 Link to comment Share on other sites More sharing options...

studiot Posted November 12, 2013 Share Posted November 12, 2013 Yes you are right. Link to comment Share on other sites More sharing options...

gabrelov Posted November 19, 2013 Share Posted November 19, 2013 Transform it to something you can do trigonometric substitution You know: LIATE Link to comment Share on other sites More sharing options...

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