Question Number 142791 by mnjuly1970 last updated on 05/Jun/21 $$\:\:\:{Evaluate}::\:… \\ $$$$\:\:\:\:\:\:\:\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{li}_{\mathrm{2}} \left(\sqrt{{x}}\:\right)}{\mathrm{1}+\sqrt{{x}}}\:{dx}=?? \\ $$$$\:\:\:\:……….. \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 77252 by Maclaurin Stickker last updated on 04/Jan/20 Commented by Maclaurin Stickker last updated on 04/Jan/20 $${I}\:{don}'{t}\:{want}\:{the}\:{answer},\:{I}\:{want}\:{a}\:{tip} \\ $$$${on}\:{how}\:{to}\:{solve}.\: \\ $$ Commented by…
Question Number 11714 by Nayon last updated on 30/Mar/17 $${Solve}\:{the}\:{Crazy}\:{equation}… \\ $$$${x}\left({lnx}\right)^{\mathrm{2}} +{xlnx}−\mathrm{1}=\mathrm{0} \\ $$ Commented by mrW1 last updated on 30/Mar/17 $$\mathrm{ln}\:{x}=\frac{\sqrt{\mathrm{1}+\frac{\mathrm{4}}{{x}}}−\mathrm{1}}{\mathrm{2}}\:\: \\ $$$${I}\:{don}'{t}\:{think}\:{there}\:{is}\:{an}\:{analytical}…
Question Number 142777 by alcohol last updated on 05/Jun/21 Commented by karannagar last updated on 05/Jun/21 $${yes}\:{i}\:{solve} \\ $$ Commented by alcohol last updated on…
Question Number 77242 by Tony Lin last updated on 04/Jan/20 $${prove}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{{a}} \sqrt{\mathrm{2}+\frac{{a}}{{x}}−\mathrm{2}\sqrt{\frac{{a}}{{x}}}\:}{dx}={a}\left[\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}{ln}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)+\mathrm{1}\right] \\ $$ Commented by mathmax by abdo last updated on…
Question Number 11707 by Nayon last updated on 30/Mar/17 $$ \\ $$$$ \\ $$$${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${pls}.\:{solve}\:{it}\:{in}\:{a}\:{alzebric}\:{way}\:, \\ $$$${that}\:{a}\:{O}\:{level}\left({ssc}\right)\:{student}\:{can} \\ $$$${understand}… \\ $$$$ \\…
Question Number 142773 by mnjuly1970 last updated on 05/Jun/21 $$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}\:……{integral}…… \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \frac{{li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{\mathrm{2}−{x}}\:{dx}=?? \\ $$$$\:…….{m}.{n}… \\ $$ Answered by mnjuly1970 last…
Question Number 11701 by Nayon last updated on 30/Mar/17 $$ \\ $$$$ \\ $$$${If}\:{X}\propto{A}\:\:\:\:{and}\:{X}\propto{B}\:, \\ $$$${then}\:{why}\:{X}\propto{AB}\:?? \\ $$$${Give}\:{me}\:{the}\:{Mathematical} \\ $$$${Explanation}…. \\ $$$$ \\ $$ Commented…
Question Number 77234 by TawaTawa last updated on 04/Jan/20 Answered by mr W last updated on 04/Jan/20 $$=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{1}}{\mathrm{5}}} …{dx} \\…
Question Number 77232 by naka3546 last updated on 04/Jan/20 $$\underset{\mathrm{0}} {\int}\overset{\mathrm{1}} {\:}\:\mathrm{ln}\:\left(\:\sqrt{{x}}\:+\:\sqrt{\mathrm{1}−{x}}\:\right)\:{dx}\:\:=\:\:? \\ $$ Answered by MJS last updated on 04/Jan/20 $$\int\mathrm{ln}\:\left(\sqrt{{x}}+\sqrt{\mathrm{1}−{x}}\right)\:{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{arcsin}\:\sqrt{{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}\left(\mathrm{1}−{x}\right)}{dt}\right] \\…