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x-5-x-2-x-6-2x-3-7-dx-




Question Number 195468 by Calculusboy last updated on 03/Aug/23
∫((x^5 +x^2 )/((x^6 +2x^3 )^7 ))dx
$$\int\frac{{x}^{\mathrm{5}} +{x}^{\mathrm{2}} }{\left({x}^{\mathrm{6}} +\mathrm{2}{x}^{\mathrm{3}} \right)^{\mathrm{7}} }{dx} \\ $$
Answered by Frix last updated on 03/Aug/23
t=x^6 +2x^3   =(1/6)∫(dt/t^7 )=−(1/(36t^6 ))=−(1/(36x^(18) (x^3 +2)^6 ))+C
$${t}={x}^{\mathrm{6}} +\mathrm{2}{x}^{\mathrm{3}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}\int\frac{{dt}}{{t}^{\mathrm{7}} }=−\frac{\mathrm{1}}{\mathrm{36}{t}^{\mathrm{6}} }=−\frac{\mathrm{1}}{\mathrm{36}{x}^{\mathrm{18}} \left({x}^{\mathrm{3}} +\mathrm{2}\right)^{\mathrm{6}} }+{C} \\ $$
Commented by Calculusboy last updated on 04/Aug/23
please solution sir
$${please}\:{solution}\:{sir} \\ $$

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