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Question Number 138335 by Ñï= last updated on 12/Apr/21

$$\int \frac{dx}{x^8+x^4+1}=?$$

Answered by MJS_new last updated on 12/Apr/21

$$x^8+x^4+1=$$$$=(x^2-x+1)(x^2+x+1)(x^2-\sqrt{3}x+1)(x^2+\sqrt{3}x+1)$$$$\mathrm{now}\mathrm{simply}\mathrm{decompose}$$$$\mathrm{I}\mathrm{get}$$$$\frac{\sqrt{3}}{12}(\ln \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1}+2(\arctan \frac{2x-1}{\sqrt{3}}+\arctan \frac{2x+1}{\sqrt{3}}))+C$$

Commented by Ñï= last updated on 12/Apr/21

$$thankyousir.$$

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