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Question Number 131520 by EDWIN88 last updated on 05/Feb/21

$$\mathrm{Nice}\mathrm{integral}$$$${\int }_0^{\mathrm{\infty }}\frac{{\mathrm{x}}^2}{{(\mathrm{x}+100)}^3}\mathrm{dx}=?$$

Commented by liberty last updated on 05/Feb/21

$$\mathrm{diverges}$$

Commented by Dwaipayan Shikari last updated on 05/Feb/21

$$Ithinkitshouldbe{\int }_0^{\mathrm{\infty }}\frac{x^2}{{(x^2+100)}^3}dx$$$$then$$$$\frac{1}{2}{\int }_0^{\mathrm{\infty }}\frac{u^{\frac{1}{2}}}{{(u+100)}^3}duu=100t$$$$=\frac{100.10}{2.{100}^3}{\int }_0^{\mathrm{\infty }}\frac{t^{\frac{3}{2}-1}}{{(t+1)}^{\frac{3}{2}+\frac{3}{2}}}dt=\frac{1}{2000}.\frac{\mathrm{\Gamma }\left(\frac{3}{2}\right)\mathrm{\Gamma }\left(\frac{3}{2}\right)}{\mathrm{\Gamma }\left(3\right)}=\frac{\pi }{16000}$$

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