Indefinite Integration

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Calculation of $\displaystyle \int\frac{1}{\left(1+x^4\right)^{\frac{1}{4}}}dx$

My Trial : $\displaystyle \int\frac{1}{x\cdot \left(x^{-4}+1\right)^{\frac{1}{4}}}dx$

Let $x^{-4}+1 = t^4$ and $\displaystyle \frac{1}{x^5}dx = -\frac{4t^3}{4}dt = -t^3dt$

$\displaystyle$

Now How can i solve after that

Thanks

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Have you tried trigonometric substitution.

with x = tan2(t)

and then use

sec2(p)= (1+tan2(p))

Edited by studiot
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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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Yes you are right.

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Transform it to something you can do trigonometric substitution

You know: LIATE

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