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Question Number 206537 by necx122 last updated on 18/Apr/24

$$\int \frac{x^4-1}{x^2\sqrt{x^4+x^2+1}}dx$$

Answered by Berbere last updated on 18/Apr/24

$$=\int \frac{x(4x^3+2x)-2x^4-2x^2-2}{2x^2\sqrt{x^4+x^2+1}}$$$$=\int \frac{x.{\left(\sqrt{x^4+x^2+1}\right)}^{\prime }}{x^2}-\frac{1.\sqrt{x^4+x^2+1}}{x^2}dx$$$$=\int d\left(\frac{\sqrt{x^4+x^2+1}}{x}\right)=\frac{\sqrt{x^4+x^2+1}}{x}+a;a\in \mathbb{R}$$$$$$

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