Question Number 147746 by 0731619 last updated on 23/Jul/21 Answered by mindispower last updated on 23/Jul/21 $$\frac{{tan}^{−} \left({x}^{\mathrm{2}} \right)}{{tan}^{−} \left({x}\right)}<\mathrm{1} \\ $$$${x}\leqslant{x}^{\mathrm{2}} <\mathrm{1},\:{and}\:{using}\:{tan}^{−} \:{increasing}\:{function} \\…
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Question Number 82185 by jagoll last updated on 19/Feb/20 $$\int\:\frac{{dx}}{\mathrm{sec}\:{x}\:+\:{csc}\:{x}}\:=\:?\: \\ $$ Commented by john santu last updated on 19/Feb/20 $$\mathrm{sec}\:{x}+\:{csc}\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}} \\ $$$$\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}\:. \\ $$$$\int\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}\:{dx}\:=\:…
Question Number 82174 by jagoll last updated on 18/Feb/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:{x}\:{ln}\left(\mathrm{sin}\:{x}\right)\:{dx}\:=\:?\: \\ $$ Commented by mathmax by abdo last updated on 19/Feb/20 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\pi}…
Question Number 16638 by tawa tawa last updated on 24/Jun/17 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\mathrm{tan}^{\mathrm{2}} \left(\mathrm{3x}\right)\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 24/Jun/17 $$\:\int_{\mathrm{0}} ^{\:\:\pi/\mathrm{4}}…
Question Number 147683 by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{let}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{2x}−\mathrm{3}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\int\:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\mathrm{en}\:\mathrm{deduire}\:\mathrm{la}\:\mathrm{decomposition}\:\mathrm{de}\:\mathrm{F}\:\mathrm{en}\:\mathrm{element}\:\mathrm{simples} \\ $$ Answered by mathmax by abdo…
Question Number 147680 by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{find}\:\mathrm{by}\:\mathrm{residus}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} }\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 147682 by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{decompose}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{n}} −\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)}\:\mathrm{dans}\:\mathrm{C}\left(\mathrm{x}\right)\:\mathrm{puis}\:\mathrm{dans}\:\mathrm{R}\left(\mathrm{x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 82139 by jagoll last updated on 18/Feb/20 $$\int\:\:\frac{\sqrt{{x}^{\mathrm{4}} +{x}^{−\mathrm{4}} +\mathrm{2}}}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$ Answered by mind is power last updated on 18/Feb/20 $${x}^{\mathrm{4}}…
Question Number 147670 by mnjuly1970 last updated on 22/Jul/21 Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\mathrm{By}\:\mathrm{definition}\:\mathrm{H}_{{n}} ^{\left(\mathrm{2}\right)} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}} } \\ $$$$\Rightarrow\:\mathrm{H}_{{n}−\mathrm{1}} ^{\left(\mathrm{2}\right)}…