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

∫((x^7 +x^3 +4)/(x^8 −x^5 +9))dx

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

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

why sir

$${why}\:{sir} \\ $$

Commented by MJS last updated on 04/Apr/20

I don′t think we can solve this

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this} \\ $$

Commented by MJS last updated on 04/Apr/20

we cannot factorize x^8 −x^5 +9

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

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

((x^7 +x^3 +4)/(x^8 −x^5 +9))=Σ_([w:w^8 −w^5 +9=0]) .((w^7 +w^3 +4)/((8w^7 −5w^4 )(x−w))) ∫((x^7 +x^3 +4)/(x^8 −x^5 +9))dx=Σ_([w:w^8 −w^5 +9=0]) ∫((w^7 +w^3 +4)/((8w^7 −5w^4 )(x−w)))dx Σ_([w:w^8 −w^5 +9]) ((w^7 +w^3 +4)/((8w^7 −5w^4 )))ln(x−w)+c

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

Commented by MJS last updated on 04/Apr/20

yes, I also found this, but I thought it was not a “solution”...

$$\mathrm{yes},\:\mathrm{I}\:\mathrm{also}\:\mathrm{found}\:\mathrm{this},\:\mathrm{but}\:\mathrm{I}\:\mathrm{thought}\:\mathrm{it}\:\mathrm{was} \\ $$$$\mathrm{not}\:\mathrm{a}\:``\mathrm{solution}''... \\ $$

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

realy is not a clear Solution

$${realy}\:{is}\:{not}\:{a}\:{clear}\:{Solution} \\ $$

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

god bless you sir

$${god}\:{bless}\:{you}\:{sir} \\ $$

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