Question Number 106098 by redmiiuser last updated on 02/Aug/20 $$\int_{\frac{\mathrm{1}}{\mathrm{2014}}} ^{\mathrm{2014}} \frac{\mathrm{tan}^{−\mathrm{1}} {x}}{{x}}\:{dx} \\ $$ Answered by abdomathmax last updated on 02/Aug/20 $$\mathrm{let}\:\mathrm{find}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\frac{\mathrm{1}}{\mathrm{a}}} ^{\mathrm{a}} \:\frac{\mathrm{arctanx}}{\mathrm{x}}\mathrm{dx}\:\:\mathrm{with}\:\mathrm{a}>\mathrm{0}…
Question Number 171620 by mokys last updated on 18/Jun/22 Commented by mokys last updated on 18/Jun/22 $${how}\:{can}\:{it}\:{proved} \\ $$ Commented by puissant last updated on…
Question Number 40544 by mondodotto@gmail.com last updated on 23/Jul/18 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\mathrm{3}^{\left(\mathrm{2}\boldsymbol{{x}}−\mathrm{1}\right)} −\mathrm{4}\left(\mathrm{3}^{\boldsymbol{{x}}} \right)+\mathrm{1}=\mathrm{0} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jul/18 $$\mathrm{3}^{\mathrm{2}{x}} .\mathrm{3}^{−\mathrm{1}}…
Question Number 171608 by SANOGO last updated on 18/Jun/22 $${montrer}\:{que} \\ $$$$\int_{{o}} ^{+{oo}} \frac{{sin}^{\mathrm{2}} {t}}{{t}^{\mathrm{2}} }{e}^{−{xt}} {dt} \\ $$$${est}\:{continu}\:{sur}\:{R}^{+} \\ $$ Answered by aleks041103 last…
Question Number 171611 by Gbenga last updated on 18/Jun/22 $$\int_{\mathrm{0}} ^{\infty} \boldsymbol{\mathrm{xe}}^{−\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{log}}^{\boldsymbol{\mathrm{n}}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{these}} \\ $$ Answered by mindispower last updated on 19/Jun/22…
Question Number 106044 by ZiYangLee last updated on 02/Aug/20 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{m},\:\mathrm{f}^{\mathrm{2}\:} \left(\mathrm{x}\right)=\mathrm{px}+\mathrm{6} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{p}. \\ $$ Answered by 1549442205PVT last updated on 02/Aug/20 $$\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{4x}^{\mathrm{2}} +\mathrm{4mx}+\mathrm{m}^{\mathrm{2}}…
Question Number 106032 by Tinku Tara last updated on 02/Aug/20 $$\mathrm{Version}\:\mathrm{2}.\mathrm{127}\:\mathrm{is}\:\mathrm{added}. \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scroll}\:\mathrm{hine}\:\mathrm{in}\:\mathrm{horizontal} \\ $$$$\:\:\:\mathrm{direction}\:\left(\mathrm{requested}\:\mathrm{by}\:\mathrm{Mr}\:\mathrm{W}\right) \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scrolls}\:\mathrm{to}\:\mathrm{new}\:\mathrm{line}\:\mathrm{to} \\ $$$$\:\:\:\mathrm{bring}\:\mathrm{newly}\:\mathrm{added}\:\mathrm{line}\:\mathrm{in}\:\mathrm{focus}. \\ $$ Commented by Tinku Tara…
Question Number 106033 by mohammad17 last updated on 02/Aug/20 Answered by mathmax by abdo last updated on 02/Aug/20 $$\mathrm{let}\:\mathrm{I}\:=\int\:\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}\mathrm{dx}\:\:\mathrm{let}\:\mathrm{decompose}\:\mathrm{F}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}\:\Rightarrow…
Question Number 171566 by SANOGO last updated on 17/Jun/22 $${prove}\:{that}\:\int_{{o}} ^{+{oo}} \frac{{sin}^{\mathrm{2}} {t}}{{t}^{\mathrm{2}} }{e}^{−{xt}} {dt}\: \\ $$$${is}\:{continious}\:{R}^{+} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 106023 by ZiYangLee last updated on 02/Aug/20 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{0}\right)\neq\mathrm{0}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\in\mathbb{R}; \\ $$$$\mathrm{2f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{y}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)+\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right),\: \\ $$$$\mathrm{express}\:\mathrm{f}\left(\mathrm{2x}\right)\:\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$ Commented by mr W last updated on 02/Aug/20 $${y}=\mathrm{0}:…