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Question Number 87371 by M±th+et£s last updated on 04/Apr/20

$$\int \frac{x^7+x^3+4}{x^8-x^5+9}dx$$

Commented by M±th+et£s last updated on 04/Apr/20

$$whysir$$

Commented by MJS last updated on 04/Apr/20

$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{think}\mathrm{we}\mathrm{can}\mathrm{solve}\mathrm{this}$$

Commented by MJS last updated on 04/Apr/20

$$\mathrm{we}\mathrm{cannot}\mathrm{factorize}{x}^8-x^5+9$$

Answered by mind is power last updated on 04/Apr/20

$$\frac{x^7+x^3+4}{x^8-x^5+9}=\sum _{[w:w^8-w^5+9=0]}.\frac{w^7+w^3+4}{(8w^7-5w^4)(x-w)}$$$$\int \frac{x^7+x^3+4}{x^8-x^5+9}dx=\sum _{[w:w^8-w^5+9=0]}\int \frac{w^7+w^3+4}{(8w^7-5w^4)(x-w)}dx$$$$\sum _{[w:w^8-w^5+9]}\frac{w^7+w^3+4}{(8w^7-5w^4)}ln(x-w)+c$$$$$$$$$$$$$$

Commented by MJS last updated on 04/Apr/20

$$\mathrm{yes},\mathrm{I}\mathrm{also}\mathrm{found}\mathrm{this},\mathrm{but}\mathrm{I}\mathrm{thought}\mathrm{it}\mathrm{was}$$$$\mathrm{not}\mathrm{a}‘‘{\mathrm{solution}}^{″}...$$

Commented by mind is power last updated on 04/Apr/20

$$realyisnotaclearSolution$$

Commented by M±th+et£s last updated on 04/Apr/20

$$godblessyousir$$

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