Question Number 1444 by 112358 last updated on 04/Aug/15 $${Evaluate}\:{the}\:{following}\:{integral}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:{n}} \lfloor{x}\rfloor^{\mathrm{1}/\lfloor{x}\rfloor!} {dx}\:\:\:\:\:\:\:\left({n}\in\mathbb{N}\right) \\ $$$${Here}\:\lfloor{x}\rfloor\:{is}\:{the}\:{integer}−{part}\:{of}\:{x} \\ $$$${e}.{g}\:\lfloor\mathrm{0}.\mathrm{12}\rfloor=\mathrm{0},\:\lfloor\mathrm{5}.\mathrm{896}\rfloor=\mathrm{5} \\ $$$$ \\ $$ Answered by…
Question Number 66959 by rajesh4661kumar@gmail.com last updated on 21/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132473 by physicstutes last updated on 14/Feb/21 $$\int\:\frac{{x}\:\mathrm{cosh}\:{x}}{\left(\mathrm{sinh}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$ Answered by mathmax by abdo last updated on 14/Feb/21 $$\mathrm{I}=\int\:\frac{\mathrm{xchx}}{\mathrm{sh}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}\:\:\mathrm{by}\:\mathrm{parts}\:\:\mathrm{u}^{'} \:=\frac{\mathrm{chx}}{\mathrm{sh}^{\mathrm{2}}…
Question Number 66938 by Cmr 237 last updated on 20/Aug/19 Commented by mathmax by abdo last updated on 21/Aug/19 $$\left.\mathrm{8}\right){by}\:{parts}\:\:\int\:{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx}\:={xln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)−\int\:{x}\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$={xln}\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 132469 by Algoritm last updated on 14/Feb/21 Answered by Olaf last updated on 15/Feb/21 $$\mathrm{Let}\:\Omega_{{i}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}_{{i}} \left(\mathrm{1}−\mathrm{ln}{x}_{{i}} \right)}{dx}_{{i}} \\ $$$$\mathrm{Let}\:{u}_{{i}} \:=\:\mathrm{1}−\mathrm{ln}{x}_{{i}}…
Question Number 132463 by EDWIN88 last updated on 14/Feb/21 $$\:\mathrm{Given}\:\int_{{a}} ^{\:{b}} \:\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}}{\mid{x}−\mathrm{3}\mid}\:\mathrm{dx}\:=\:\frac{\mathrm{11}}{\mathrm{2}}\:\mathrm{where}\:\begin{cases}{{a}<\mathrm{3}<{b}}\\{{a}+\mathrm{2}{b}=\mathrm{8}}\end{cases} \\ $$$$\:\mathrm{Find}\:\int_{{a}} ^{{b}} \:\mid{x}\mid\:\mathrm{dx}.\: \\ $$ Answered by bemath last updated on…
Question Number 1350 by 112358 last updated on 24/Jul/15 $${Evaluate}\:{the}\:{following}\:{integral}: \\ $$$${I}=\int_{\pi/\mathrm{4}} ^{\:\pi/\mathrm{2}} \left({cos}\mathrm{2}{x}+{sin}\mathrm{2}{x}\right){ln}\left({cosx}+{sinx}\right)\:{dx} \\ $$ Commented by prakash jain last updated on 25/Jul/15 $$\int\mathrm{sin}\:\mathrm{2}{x}\mathrm{ln}\:\left(\mathrm{cos}\:{x}+\mathrm{sin}\:{x}\right){dx}…
Question Number 132414 by john_santu last updated on 14/Feb/21 Commented by john_santu last updated on 14/Feb/21 $$\underline{\mathrm{super}\:\mathrm{nice}\:\mathrm{integral}}\: \\ $$ Answered by liberty last updated on…
Question Number 132410 by bramlexs22 last updated on 14/Feb/21 $$\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$ Answered by EDWIN88 last updated on 14/Feb/21 $$\mathrm{I}=\int_{\mathrm{0}}…
Question Number 132392 by physicstutes last updated on 14/Feb/21 $$\:\mathcal{I}\:=\:\int{e}^{\mathrm{cos}^{−\mathrm{1}} {x}} {dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com