Question Number 186310 by normans last updated on 03/Feb/23
![((∫x(x^2 +5)^(1/2) dx − 3∫x(x^2 +5)^(−1/2) dx)/(∫ ((x[(x^2 +5)−3])/( (√(x^2 +5 )))) dx)) =??](https://www.tinkutara.com/question/Q186310.png)
$$ \\ $$$$\:\:\:\frac{\int\boldsymbol{{x}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)^{\mathrm{1}/\mathrm{2}} \boldsymbol{{dx}}\:−\:\mathrm{3}\int\boldsymbol{{x}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)^{−\mathrm{1}/\mathrm{2}} \:\boldsymbol{{dx}}}{\int\:\:\frac{\boldsymbol{{x}}\left[\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)−\mathrm{3}\right]}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\:\:}}\:\boldsymbol{{dx}}}\:=??\:\:\:\: \\ $$$$ \\ $$
Answered by Frix last updated on 03/Feb/23
$$=\mathrm{1}+\frac{\mathrm{3}\left(\mathrm{C}_{\mathrm{1}} −{C}_{\mathrm{2}} −{C}_{\mathrm{3}} \right)}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}+\mathrm{3}{C}_{\mathrm{3}} } \\ $$