Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 131058 by pipin last updated on 01/Feb/21

∫(((x^2 +2)(x^2 +3)(x^2 +4))/((x^2 +5)(x^2 +6)(x^2 +7))) dx

$$\int\frac{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4}\right)}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{5}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{6}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{7}\right)}\:\mathrm{dx}\: \\ $$

Answered by MJS_new last updated on 01/Feb/21

=∫1−(3/(x^2 +5))+((24)/(x^2 +6))−((30)/(x^2 +7))dx=  =x−((3(√5))/5)arctan (((√5)x)/5) +4(√6)arctan (((√6)x)/6) −((30(√7))/7)arctan (((√7)x)/7) +C

$$=\int\mathrm{1}−\frac{\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{5}}+\frac{\mathrm{24}}{{x}^{\mathrm{2}} +\mathrm{6}}−\frac{\mathrm{30}}{{x}^{\mathrm{2}} +\mathrm{7}}{dx}= \\ $$$$={x}−\frac{\mathrm{3}\sqrt{\mathrm{5}}}{\mathrm{5}}\mathrm{arctan}\:\frac{\sqrt{\mathrm{5}}{x}}{\mathrm{5}}\:+\mathrm{4}\sqrt{\mathrm{6}}\mathrm{arctan}\:\frac{\sqrt{\mathrm{6}}{x}}{\mathrm{6}}\:−\frac{\mathrm{30}\sqrt{\mathrm{7}}}{\mathrm{7}}\mathrm{arctan}\:\frac{\sqrt{\mathrm{7}}{x}}{\mathrm{7}}\:+{C} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com