Question Number 207906 by nachosam last updated on 30/May/24 $${help} \\ $$$$\int_{\mathrm{1}} ^{\:\infty} {x}^{−{ln}\left({x}\right)} {dx} \\ $$$$ \\ $$ Answered by Berbere last updated on…
Question Number 207878 by luciferit last updated on 29/May/24 Answered by Berbere last updated on 30/May/24 $${not}\:{well}\:{defind} \\ $$$$\left.{g}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} {f}\left({t}^{\mathrm{4}} \right)+\mathrm{4}{t}^{\mathrm{4}} {f}'\left({t}\right)\right){dt}? \\ $$$$…
Question Number 207857 by necx122 last updated on 28/May/24 $$\int{x}\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$ Answered by Ghisom last updated on 28/May/24 $$\mathrm{by}\:\mathrm{parts} \\ $$$$\int{x}\mathrm{arctan}\:{x}\:{dx}= \\ $$$$=\frac{{x}^{\mathrm{2}}…
Question Number 207789 by Ghisom last updated on 26/May/24 $$\forall{r}\in\mathbb{R}:\:{H}_{{r}} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{t}^{{r}} −\mathrm{1}}{{t}−\mathrm{1}}{dt} \\ $$$${H}_{{r}+\mathrm{2}} −{H}_{{r}} =\mathrm{1} \\ $$$${r}=? \\ $$ Answered by MM42…
Question Number 207753 by efronzo1 last updated on 25/May/24 Answered by Berbere last updated on 25/May/24 $${A}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\frac{{k}+\mathrm{1}−{k}}{{k}\left({k}+\mathrm{1}\right)}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\frac{\mathrm{1}}{{k}}−\frac{\mathrm{1}}{{k}+\mathrm{1}} \\ $$$$=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2024}}=\frac{\mathrm{2023}}{\mathrm{2024}}…
Question Number 207707 by justenspi last updated on 23/May/24 $$\underset{\mathrm{0}} {\overset{+\infty} {\int}}\frac{\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)}{\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)+\left({x}\mathrm{cos}\:\left({x}\right)+\mathrm{sin}\:\left({x}\right)\right)^{\mathrm{2}} }{d}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 207652 by universe last updated on 22/May/24 $$\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{log}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx}\:\:=\:?{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{log}\:\left(\mathrm{1}+{x}^{\mathrm{4}} \right){dx}\:=\:? \\ $$$$\:\:\mathrm{and}\:\mathrm{if}\:\mathrm{possible}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{p} \\ $$$$\:\mathrm{p}\:\:\:=\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{log}\left(\mathrm{1}+{x}^{{n}} \right){dx}\:=\:?\:\:\:\:\:\:{n}\in\mathbb{N} \\ $$…
Question Number 207620 by Ghisom last updated on 21/May/24 $$\mathrm{prove}\:\mathrm{that}\:\underset{−{a}} {\overset{{a}} {\int}}\:\frac{{dx}}{{x}^{{n}} +\mathrm{1}+\sqrt{{x}^{\mathrm{2}{n}} +\mathrm{1}}}={a} \\ $$ Answered by Berbere last updated on 21/May/24 $$\int_{−{a}} ^{{a}}…
Question Number 207582 by sniper237 last updated on 19/May/24 $$\int_{\mathrm{0}} ^{\pi} \:{ln}\left({sinx}\right){dx}=−\pi{ln}\mathrm{2} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\Gamma\left({x}\right){dx}\:=\:{ln}\left(\mathrm{2}\pi\right) \\ $$ Answered by mathzup last updated on 21/May/24…
Question Number 207565 by mathzup last updated on 18/May/24 $${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}^{\mathrm{2}} }{{tan}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by sniper237 last updated on 19/May/24 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}}…