Question Number 190168 by TUN last updated on 29/Mar/23
$$\left.\mathrm{1}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{sin}\:{x}}{{x}^{{p}} +{sin}\:{x}}{dx}\:,{p}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\underset{\pi} {\int}^{\infty} \frac{{xcos}\:{x}}{{x}^{{p}} +{x}^{{q}} }{dx},{p}>\mathrm{0}{and}\:{q}>\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{sin}\:{x}^{{p}} }{\:{x}^{{q}} }{dx},\:{p}>\mathrm{0},{q}>\mathrm{0} \\ $$$$\left.\mathrm{4}\right)\underset{\mathrm{0}} {\int}^{\mathrm{2}} \frac{{dx}}{\mid{ln}\:{x}\mid^{{p}} }\:,{p}>\mathrm{0} \\ $$$$\left.\mathrm{5}\right)\underset{\mathrm{0}} {\int}^{\mathrm{1}} \frac{{cos}\frac{\mathrm{1}}{\mathrm{1}−{x}}}{\:\sqrt[{{n}}]{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$$\left.\mathrm{6}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{dx}}{{x}^{{p}} \sqrt[{\mathrm{3}}]{{sin}^{\mathrm{2}} {x}}} \\ $$
Commented by senestro last updated on 30/Mar/23
$${how}\:{can}\:{we}\:{solve}\:{it}? \\ $$
Commented by TUN last updated on 01/Apr/23
$${It}'{s}\:{the}\:{improper}\:{integral} \\ $$