Question Number 85793 by M±th+et£s last updated on 24/Mar/20 $$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{tan}^{−\mathrm{1}} \left({x}−\mathrm{1}\right)\:{ln}\left({x}−\mathrm{1}\right)}{{x}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20256 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left({x}−\mathrm{4}\right)\sqrt{{x}+\mathrm{3}}} \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${x}\:+\:\mathrm{3}\:=\:{t}^{\mathrm{2}} \\ $$$${dx}\:=\:\mathrm{2}{tdt} \\ $$$${x}\:−\:\mathrm{4}\:=\:{t}^{\mathrm{2}} \:−\:\mathrm{7}…
Question Number 20255 by tammi last updated on 24/Aug/17 $$\int\frac{{x}^{\mathrm{3}} {dx}}{\:\sqrt{{x}−\mathrm{1}}} \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${x}\:−\:\mathrm{1}\:=\:{t}^{\mathrm{2}} \\ $$$${dx}\:=\:\mathrm{2}{tdt} \\ $$$${x}^{\mathrm{3}}…
Question Number 20254 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $${Let}\:{x}−\mathrm{1}=\frac{\mathrm{1}}{{t}} \\ $$$$\Rightarrow{dx}=\frac{−\mathrm{1}}{{t}^{\mathrm{2}} }{dt} \\…
Question Number 85789 by Rio Michael last updated on 24/Mar/20 $$\int\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:= \\ $$ Answered by sakeefhasan05@gmail.com last updated on 24/Mar/20 $$=\left(\mathrm{ln}\:\mathrm{x}\right)^{\mathrm{2}} .\mathrm{x}\:−\int\mathrm{x}.\mathrm{2}\left(\mathrm{ln}\:\mathrm{x}\right).\frac{\mathrm{1}}{\mathrm{x}}\mathrm{dx} \\ $$$$=\mathrm{x}\left(\mathrm{ln}\:\mathrm{x}\right)^{\mathrm{2}}…
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Question Number 85786 by Cmr 237 last updated on 24/Mar/20 $${posons}\: \\ $$$$\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} =\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} +\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \sqrt{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{montre}}\:\boldsymbol{\mathrm{que}}\:\boldsymbol{\mathrm{pgcd}}\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{{b}}_{\boldsymbol{{n}}} \right)=\mathrm{1} \\ $$ Terms of Service…
Question Number 151322 by mathdanisur last updated on 20/Aug/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{pairs}\:\:\left(\mathrm{x};\mathrm{y}\right)\:\:\mathrm{of}\:\mathrm{integers} \\ $$$$\mathrm{which}\:\mathrm{satisfy}: \\ $$$$\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{3x}\:+\:\mathrm{y}\:=\:\mathrm{0} \\ $$ Commented by mathdanisur last updated on 20/Aug/21 $$\mathrm{with}\:\boldsymbol{\mathrm{x}}\:\mathrm{real},\:\boldsymbol{\mathrm{y}}\:\mathrm{integer}…
Question Number 151317 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}=\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}\:-\:\sqrt{\mathrm{6}}}\:+\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}\:+\:\sqrt{\mathrm{6}}} \\ $$$$\mathrm{find}\:\:\mathrm{E}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{6}} \:-\:\mathrm{6x}^{\mathrm{4}} \:+\:\mathrm{9x}^{\mathrm{2}} \:=\:? \\ $$ Answered by iloveisrael last updated on 20/Aug/21 $$\:{we}\:{have}\:{x}−\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}−\sqrt{\mathrm{6}}}−\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}+\sqrt{\mathrm{6}}}\:=\:\mathrm{0}…
Question Number 151316 by iloveisrael last updated on 20/Aug/21 $$\:\:\:\:\:\:{Find}\:{positive}\:{integers}\: \\ $$$$\:\:\:\:\:{a}\:{and}\:{b}\:{such}\:{that}\: \\ $$$$\:\:\:\:\:\left(\sqrt[{\mathrm{3}}]{{a}}\:+\sqrt[{\mathrm{3}}]{{b}}\:−\mathrm{1}\right)^{\mathrm{2}} =\:\mathrm{49}+\:\mathrm{20}\sqrt[{\mathrm{3}}]{\mathrm{6}}\: \\ $$ Answered by Rasheed.Sindhi last updated on 20/Aug/21 $$\overset{\mathcal{SOLVE}\:\:{for}\:{a},{b}\in\mathbb{Z}^{+}…