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Indefinite Integration

stuart clark

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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





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Have you tried trigonometric substitution.

with x = tan2(t)


and then use

sec2(p)= (1+tan2(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

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