Question Number 150655 by mnjuly1970 last updated on 14/Aug/21 Answered by Ar Brandon last updated on 14/Aug/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−\sqrt{{x}}} \mathrm{ln}\left(\sqrt{{x}}\right)}{{x}^{\frac{\mathrm{1}}{\mathrm{4}}} }{dx}\underset{{x}={u}^{\mathrm{2}} } {=}\mathrm{2}\int_{\mathrm{0}} ^{\infty}…
Question Number 150647 by puissant last updated on 14/Aug/21 Answered by puissant last updated on 14/Aug/21 $${posons}\:\:{I}_{\mathrm{2}{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({sint}\right)^{\mathrm{2}{n}} {dt} \\ $$$$=\frac{\mathrm{1}×\mathrm{3}×\mathrm{5}……×\left(\mathrm{2}{n}−\mathrm{1}\right)}{\mathrm{2}×\mathrm{4}×\mathrm{6}×…..×\mathrm{2}{n}}×\frac{\pi}{\mathrm{2}} \\ $$$$\Rightarrow\:\:{I}_{\mathrm{2}{n}}…
Question Number 85097 by jagoll last updated on 19/Mar/20 $$\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{8} \\ $$$$\mathrm{find}\:\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last…
Question Number 150627 by puissant last updated on 14/Aug/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(−\mathrm{1}\right)^{{E}\left(\frac{\mathrm{1}}{{x}}\right)} {dx}}{{x}} \\ $$ Answered by puissant last updated on 14/Aug/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(−\mathrm{1}\right)^{{E}\left(\frac{\mathrm{1}}{{x}}\right)}…
Question Number 85059 by Power last updated on 18/Mar/20 Answered by MJS last updated on 18/Mar/20 $${x}^{\mathrm{5}} +\mathrm{1}= \\ $$$$=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right) \\ $$$$\mathrm{you}'\mathrm{ll}\:\mathrm{have}\:\mathrm{to}\:\mathrm{decompose}\:\mathrm{and}\:\mathrm{then}\:\mathrm{use} \\…
Question Number 85009 by mathmax by abdo last updated on 18/Mar/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{{n}} }{{sh}\left({x}\right)}{dx}\:{with}\:{n}\:{integr}\:{natural} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 150533 by mnjuly1970 last updated on 13/Aug/21 $$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{solve}… \\ $$$$\:\:\mathrm{I}:=\:\int_{−\infty} ^{\:\infty} {e}^{\:{x}−{n}.{sinh}^{\:\mathrm{2}} \left({x}\right)} {dx}\:\overset{??} {=}\sqrt{\frac{\pi}{{n}}} \\ $$$$\:\:\:\:\:\:\:…{m}.{n}… \\ $$ Answered by…
Question Number 19457 by NEC last updated on 11/Aug/17 $${prove}\:{that}\:\int\mathrm{tan}\:^{\mathrm{2}} {xdx} \\ $$$$ \\ $$$$=\mathrm{tan}\:{x}−{x} \\ $$ Answered by Joel577 last updated on 11/Aug/17 $$\int\:\mathrm{tan}^{\mathrm{2}}…
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Question Number 84957 by john santu last updated on 17/Mar/20 $$\int\:\left(\mathrm{2}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} \:\mathrm{dx}\:=\: \\ $$ Commented by john santu last updated on 17/Mar/20 $$\int\:\left(\mathrm{8}−\mathrm{3}\left(\mathrm{4x}^{\mathrm{2}} \right)+\mathrm{3}\left(\mathrm{2x}^{\mathrm{4}}…