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Question Number 190168 by TUN last updated on 29/Mar/23

$$1){\underset{0}{\int }}^{\mathrm{\infty }}\frac{sinx}{x^p+sinx}dx,p>0$$ $$2){\underset{\pi }{\int }}^{\mathrm{\infty }}\frac{xcosx}{x^p+x^q}dx,p>0andq>0$$ $$3){\underset{0}{\int }}^{\mathrm{\infty }}\frac{sin{x}^p}{x^q}dx,p>0,q>0$$ $$4){\underset{0}{\int }}^2\frac{dx}{\mid lnx{\mid }^p},p>0$$ $$5){\underset{0}{\int }}^1\frac{cos\frac{1}{1-x}}{\sqrt[n]{1-x^2}}dx$$ $$6){\underset{0}{\int }}^{\mathrm{\infty }}\frac{dx}{x^p\sqrt[3]{{sin}^{2}x}}$$

Commented bysenestro last updated on 30/Mar/23

$$howcanwesolveit?$$

Commented byTUN last updated on 01/Apr/23

$${It}^{\prime }stheimproperintegral$$

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