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$$\int \dfrac{1+x^4}{(1-x^4)^{3/2}} dx$$

Attempt:

Multiplied and divided numerator by $x^2 $ to get $\displaystyle\int \dfrac{x^2+x^6}{(x^3 - x^7)^{3/2}} dx$ but the problem here is the $-$ sign before $x^7$ otherwise the numerator would have been the derivative and I could've done u- substitution.

How do I proceed with it? Need a minor hint.

Archer
  • 6,051

1 Answers1

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Factor out a minus sign and write the numerator as $-2 + (1 - x^4)$, then you have $\int {-2 + y \over y^{3/2}} dx$ and continue to get...

$\frac{x}{\sqrt{1-x^4}}$.

David G. Stork
  • 29,774