Question Number 78269 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:{with} \\ $$$${a}>\mathrm{0}\:\:{find}\:\:\:\int_{\mathrm{1}} ^{\mathrm{2}} {f}\left({a}\right){da} \\ $$ Commented by…
Question Number 78264 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\pi} {x}\:{cos}^{\mathrm{4}} {x}\:{dxand}\:{J}=\int_{\mathrm{0}} ^{\pi} {x}\:{sin}^{\mathrm{4}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}+{J}\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:{I}\:{and}\:{J} \\ $$…
Question Number 78267 by msup trace by abdo last updated on 15/Jan/20 $${find}\:\:\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} −{x}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by mathmax by abdo…
Question Number 78265 by msup trace by abdo last updated on 15/Jan/20 $${find}\:\int\:\:\frac{{sin}^{\mathrm{3}} {x}}{{tan}^{\mathrm{5}} {x}}{dx} \\ $$ Answered by jagoll last updated on 15/Jan/20 $$\int\mathrm{sin}\:^{\mathrm{3}}…
Question Number 78254 by mind is power last updated on 15/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{xln}\left(\mathrm{ln}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$$$\mathrm{i}\:\mathrm{poste}\:\mathrm{solution}\:\mathrm{later}! \\ $$ Terms of Service Privacy Policy…
Question Number 78251 by aliesam last updated on 15/Jan/20 $$\int\frac{{x}+\mathrm{4}}{{x}−\sqrt[{\mathrm{3}}]{{x}}}\:{dx}\: \\ $$ Answered by john santu last updated on 15/Jan/20 $${let}\:{x}\:=\:{u}^{\mathrm{3}} \:\Rightarrow{dx}=\mathrm{3}{u}^{\mathrm{2}} \:{du} \\ $$$$\int\:\frac{{u}^{\mathrm{3}}…
Question Number 12702 by mad last updated on 29/Apr/17 $${find}\:\int{cos}^{\mathrm{2}} \mathrm{2}{x}\:{dx} \\ $$ Answered by Joel577 last updated on 29/Apr/17 $$\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\:=\:\frac{\mathrm{1}\:+\:\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{2}} \\ $$$$\int\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\:{dx}…
Question Number 143755 by Ar Brandon last updated on 18/Jun/21 $$\mathrm{Study}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to} \\ $$$$\alpha\:\mathrm{and}\:\beta\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral}\:\mathrm{below}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{x}^{\alpha} \left(\mathrm{lnx}\right)^{\beta} } \\ $$ Answered by mathmax by…
Question Number 78198 by john santu last updated on 15/Jan/20 Commented by john santu last updated on 15/Jan/20 $${dear}\:{Mjs}\:{sir}. \\ $$$${i}\:{ask}\:{for}\:{your}\:{opinion}\:{on}\:{this}\:{answer}? \\ $$$${right}\:{or}\:{not}. \\ $$…
Question Number 143735 by mnjuly1970 last updated on 17/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{Calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\:\int_{−\infty} ^{\:\infty} \frac{{dx}}{{x}^{\:\mathrm{2}} \:{e}^{\frac{{a}}{{x}^{\mathrm{2}} }} }\:=?\:\:\left({a}\:>\:\mathrm{0}\:\right) \\ $$ Answered by Dwaipayan Shikari…