Question Number 758 by 13/NaSaNa(N)056565 last updated on 08/Mar/15 $$\int{x}\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$$$ \\ $$ Commented by malwaan last updated on 08/Mar/15 $${integral}\:{by}\:{parts} \\ $$$$\int{udv}={uv}−\int{vdu}\:…
Question Number 757 by 123456 last updated on 07/Mar/15 $${k}\frac{{d}^{\mathrm{2}} {i}}{{dt}^{\mathrm{2}} }+{l}\frac{{di}}{{dt}}+{ri}={v} \\ $$$${i}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${i}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${k},{l},{r},{v}\:{are}\:{constants} \\ $$ Commented by prakash jain last…
Question Number 66293 by Rio Michael last updated on 12/Aug/19 $${What}\:{do}\:{we}\:{mean}\:{by}\:\: \\ $$$$\:\:\int_{−\infty} ^{+\infty} {f}\left({x}\right)\:{dx}? \\ $$ Commented by mathmax by abdo last updated on…
Question Number 131825 by liberty last updated on 09/Feb/21 $$\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2n}−\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }\:? \\ $$ Answered by mr W last updated on 09/Feb/21 $${method}\:\mathrm{1} \\…
Question Number 66290 by hmamarques1994@gmail.com last updated on 12/Aug/19 $$\:\sqrt[{\sqrt{\mathrm{3}}}]{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:+\:\boldsymbol{\mathrm{x}}^{\sqrt{\mathrm{3}}} \:−\:\mathrm{392}\:=\:\mathrm{0} \\ $$ Answered by Tanmay chaudhury last updated on 12/Aug/19 $$\left({x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}} +{x}^{\sqrt{\mathrm{3}}}…
Question Number 131827 by Salman_Abir last updated on 09/Feb/21 Answered by liberty last updated on 09/Feb/21 $$\left.\:=\:\mathrm{ln}\:\mid\mathrm{tan}\:\mathrm{x}\mid\:\right]_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:=\:\mathrm{ln}\:\mid\mathrm{tan}\:\frac{\pi}{\mathrm{3}}\mid−\mathrm{ln}\:\mid\mathrm{tan}\:\frac{\pi}{\mathrm{4}}\mid \\ $$$$\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\left(\mathrm{3}\right) \\ $$ Terms of…
Question Number 752 by 112358 last updated on 06/Mar/15 $${Show}\:{that}\:,\:\forall{b}\in{R}^{+} ,\: \\ $$$${tan}^{−\mathrm{1}} {b}+{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{b}}=\frac{\pi}{\mathrm{2}}\:. \\ $$ Answered by 123456 last updated on 06/Mar/15 $${lets}\:{f}\left({x}\right):=\mathrm{arctan}\:{x}+\mathrm{arctan}\:\frac{\mathrm{1}}{{x}},{x}>\mathrm{0}…
Question Number 751 by 112358 last updated on 06/Mar/15 $${Determine}\:{the}\:{number}\:{of}\:{integral} \\ $$$${factors}\:{of}\:\mathrm{105840},\:{excluding}\:\mathrm{1}\: \\ $$$${and}\:\mathrm{105840}. \\ $$$$ \\ $$$$ \\ $$ Answered by prakash jain last…
Question Number 131820 by mr W last updated on 09/Feb/21 Commented by liberty last updated on 09/Feb/21 $$\frac{\mathrm{x}}{\mathrm{2}}=\:\frac{\mathrm{3}}{\mathrm{1}}\Rightarrow\mathrm{x}=\mathrm{6} \\ $$$$\mathrm{x}.\mathrm{1}\:=\:\mathrm{2}.\mathrm{3}\:\Rightarrow\mathrm{x}=\mathrm{6} \\ $$$$\frac{\mathrm{3}}{\mathrm{x}}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow\mathrm{x}=\mathrm{6} \\ $$ Commented…
Question Number 66287 by Tony Lin last updated on 12/Aug/19 $$\mathrm{10}^{\mathrm{10}^{\mathrm{10}^{.\centerdot^{.\mathrm{10}} } } } =?\: \\ $$ Answered by MJS last updated on 12/Aug/19 $$+\infty…