Question Number 125684 by mnjuly1970 last updated on 13/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:\mathrm{INTEGRAL}… \\ $$$$\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{3}} \left\{{ln}\left(\mathrm{1}+{e}^{{x}} \right)\:−{x}\right\}{dx}=\frac{\mathrm{45}}{\mathrm{8}}\:\zeta\left(\:\mathrm{5}\:\right) \\ $$$$ \\ $$ Answered by Dwaipayan…
Question Number 191188 by cortano12 last updated on 20/Apr/23 $$\:\:\:\:\:\:\:\:\:\:\:\int\:\sqrt[{\mathrm{4}}]{\frac{\mathrm{2}−\mathrm{x}}{\mathrm{1}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$ Answered by mehdee42 last updated on 20/Apr/23 $$\sqrt[{\mathrm{4}}]{\frac{\mathrm{2}−{x}}{\mathrm{1}−{x}}}={u}\Rightarrow{x}=\frac{{u}^{\mathrm{4}} −\mathrm{2}}{{u}^{\mathrm{4}} −\mathrm{1}}\Rightarrow{dx}=\frac{\mathrm{4}{u}^{\mathrm{3}} }{\left({u}^{\mathrm{4}} −\mathrm{1}\right)^{\mathrm{2}} \:}\:{du}…
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Question Number 60050 by maxmathsup by imad last updated on 17/May/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{\mathrm{3}} −\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 60036 by sitangshu17 last updated on 17/May/19 Answered by tanmay last updated on 17/May/19 $${x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}>\mathrm{0} \\ $$$$\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)>\mathrm{0} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6} \\ $$$${when}\:…
Question Number 60027 by aliesam last updated on 17/May/19 $$\int{x}^{{i}} {dx}=? \\ $$ Answered by MJS last updated on 17/May/19 $$\int{x}^{\mathrm{i}} {dx}=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{i}}{x}^{\mathrm{1}+\mathrm{i}} +{C}=\frac{\mathrm{1}−\mathrm{i}}{\mathrm{2}}{x}^{\mathrm{1}+\mathrm{i}} \\ $$…
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Question Number 125542 by TITA last updated on 11/Dec/20 $$\int{x}^{\mathrm{7}} \sqrt{\mathrm{1}−{x}^{\mathrm{3}} }{dx}=? \\ $$ Commented by TITA last updated on 11/Dec/20 $${please}\:{help} \\ $$ Answered…
Question Number 59999 by Mr X pcx last updated on 16/May/19 $${let}\:{U}_{{n}} \:\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{calvulate}\:\:{lim}_{{n}\rightarrow+\infty} \:\:\:{U}_{{n}}…
Question Number 59998 by Mr X pcx last updated on 16/May/19 $${find}\:\int\:\frac{{dx}}{{acosx}\:+{bsinx}}\:\:{with}\:{a}\:{and}\:{b}\:{reals} \\ $$ Commented by mr W last updated on 16/May/19 $${a}\:\mathrm{cos}\:{x}+{b}\:\mathrm{sin}\:{x}=\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\left(\frac{{a}}{\:\sqrt{{a}^{\mathrm{2}}…