Question Number 54259 by 951172235v last updated on 01/Feb/19 Commented by Meritguide1234 last updated on 01/Feb/19 Answered by rahul 19 last updated on 01/Feb/19 $$\mathrm{1}.…
Question Number 119784 by bemath last updated on 27/Oct/20 $$\:\:\int\:\frac{{dx}}{\:\sqrt{\left(\mathrm{4}{x}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$$$ \\ $$ Answered by bobhans last updated on 27/Oct/20 $$\int\:\frac{{dx}}{\:\left(\mathrm{4}−\left(\mathrm{2}−{x}\right)^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 54248 by rahul 19 last updated on 01/Feb/19 Commented by rahul 19 last updated on 01/Feb/19 $$\left.{Ans}.\:{for}\:\mathrm{3}\right)\rightarrow\:\mathrm{2}\pi^{\mathrm{2}} . \\ $$$$\left.{for}\:\mathrm{2}\right)\rightarrow\:{put}\:{x}=\mathrm{tan}\theta\:{and}\:{then}\:{use} \\ $$$${the}\:{property}\:{of}\:{replacing}\:{x}\:{by}\:{a}+{b}−{x}. \\…
Question Number 54240 by 951172235v last updated on 01/Feb/19 Commented by rahul 19 last updated on 01/Feb/19 $${a}=\mathrm{2}\:,\:{b}=\mathrm{3},{c}=\mathrm{8},{d}=\mathrm{2008}. \\ $$ Answered by rahul 19 last…
Question Number 119773 by bemath last updated on 26/Oct/20 $$\underset{−\mathrm{4}} {\overset{\mathrm{4}} {\int}}\:{x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}} \:}\:\mathrm{sec}\:{x}\:{dx}\: \\ $$ Answered by MJS_new last updated on 27/Oct/20 $${f}\left({x}\right)={x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}}…
Question Number 119762 by mathmax by abdo last updated on 26/Oct/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{x}^{\mathrm{4}} \mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{8}} } \\ $$ Answered by Olaf last updated on…
Question Number 54224 by rahul 19 last updated on 31/Jan/19 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin}{x}+\mathrm{cos}{x}}{\mathrm{16}+\mathrm{9sin2}{x}}\:{dx}\:=? \\ $$ Commented by Meritguide1234 last updated on 01/Feb/19 $$\Rightarrow\int_{\mathrm{0}} ^{\pi/\mathrm{4}} \frac{\mathrm{sinx}+\mathrm{cosx}}{\mathrm{25}−\mathrm{9}\left(\mathrm{sinx}−\mathrm{cosx}\right)^{\mathrm{2}}…
Question Number 119752 by Bird last updated on 26/Oct/20 $${find}\:{I}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ch}\left(\mathrm{1}+\lambda{cosx}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left(\lambda\:{real}\:>\mathrm{0}\right) \\ $$ Answered by mathmax by abdo last…
Question Number 185284 by Mingma last updated on 19/Jan/23 Answered by MJS_new last updated on 20/Jan/23 $$\mathrm{one}\:\mathrm{method}: \\ $$$$\int\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{3}} \:{x}\:+\mathrm{cos}^{\mathrm{3}} \:{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\:\rightarrow\:{dx}=−\frac{{dt}}{\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}\right] \\ $$$$=−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\frac{\mathrm{2}{t}^{\mathrm{2}}…
Question Number 119750 by 675480065 last updated on 26/Oct/20 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{1019}} {\prod}}\left[\frac{\mathrm{2k}}{\mathrm{2k}−\mathrm{1}}\right]=? \\ $$ Answered by Bird last updated on 26/Oct/20 $$\prod_{{k}=\mathrm{1}} ^{\mathrm{1019}} \left[\frac{\mathrm{2}{k}}{\mathrm{2}{k}−\mathrm{1}}\right]\:=\prod_{{k}=\mathrm{1}} ^{\mathrm{1019}}…