Question Number 118905 by benjo_mathlover last updated on 20/Oct/20 $$\:\:\:\int\:\frac{{d}\lambda}{\left(\lambda^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{2}} }\:=?\: \\ $$ Answered by Bird last updated on 21/Oct/20 $${I}=\int\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{2}} }\:\Rightarrow{I}=\int\:\frac{{dx}}{\left({x}−\mathrm{3}\right)^{\mathrm{2}} \left({x}+\mathrm{3}\right)^{\mathrm{2}}…
Question Number 118891 by cantor last updated on 20/Oct/20 $$\:\int_{\mathrm{0}} ^{\pi} \boldsymbol{{arctan}}\left(\mathrm{3}^{\boldsymbol{{cosx}}} \right)\boldsymbol{{dx}}=??? \\ $$$$ \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{help}} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 118886 by mnjuly1970 last updated on 20/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:\:{advanced}\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{evaluate}\:::\:\:\left\{_{\mathrm{2}.\:\Omega_{\mathrm{2}} =\:\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{{x}}\:{dx}=??} ^{\mathrm{1}.\:\Omega_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{{x}}{dx}=??} \right. \\…
Question Number 118834 by bramlexs22 last updated on 20/Oct/20 $$\:\:\int\:\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{4}{x}^{\mathrm{3}} }\:{dx}\: \\ $$ Answered by bobhans last updated on 20/Oct/20 $$\:{Solve}\:\int\:\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{4}{x}^{\mathrm{3}}…
Question Number 53295 by gunawan last updated on 20/Jan/19 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\mathrm{2}+\mathrm{cos}\:{x}}\:{dx}=… \\ $$ Commented by maxmathsup by imad last updated on 20/Jan/19 $${changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give}\: \\…
Question Number 53293 by gunawan last updated on 20/Jan/19 $$\int_{−\mathrm{1}/\mathrm{2}} ^{\mathrm{1}/\mathrm{2}} \mid{x}\mathrm{cos}\:\frac{\pi{x}}{\mathrm{2}}\mid\:{dx}=… \\ $$ Commented by maxmathsup by imad last updated on 20/Jan/19 $${we}\:{have}\:{f}\left({x}\right)=\mid{xcos}\left(\frac{\pi{x}}{\mathrm{2}}\right)\mid=\mid{x}\mid\mid{cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)\mid\:{is}\:{a}\:{even}\:{function}\:{so} \\…
Question Number 53294 by gunawan last updated on 20/Jan/19 $$\int_{−\mathrm{1}/\mathrm{2}} ^{\mathrm{1}/\mathrm{2}} \left[\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{\mathrm{2}} −\mathrm{2}\right]^{\mathrm{1}/\mathrm{2}} {dx}=… \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19 $${f}\left({x}\right)=\left[\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{2}}…
Question Number 53292 by gunawan last updated on 20/Jan/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{x}^{\mathrm{2}} } {dx}=.. \\ $$ Commented by maxmathsup by imad last updated on 20/Jan/19…
Question Number 53284 by maxmathsup by imad last updated on 20/Jan/19 $${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({xt}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:{x}\:{real}\:. \\ $$ Commented by prof Abdo imad last updated on…
Question Number 53285 by maxmathsup by imad last updated on 20/Jan/19 $${let}\:{I}_{\lambda} \:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{xdx}}{{cos}^{\mathrm{2}} {x}\:+\lambda^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}\:\:{with}\:\lambda\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{I}_{\lambda} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{xdx}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}}…