Question Number 31296 by abdo imad last updated on 05/Mar/18 $${find}\:\:\int_{\mathrm{0}} ^{+\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1}\:. \\ $$ Commented by NECx last updated on 07/Mar/18 $${thats}\:{the}\:{greatest}\:{lie}\:{of}\:{the}\:{century}.…
Question Number 162365 by mathlove last updated on 29/Dec/21 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{ln}^{\mathrm{2}} \left({x}+{y}+{z}\right){dxdydz}=? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 162348 by smallEinstein last updated on 29/Dec/21 Commented by mr W last updated on 29/Dec/21 $${Einstein}\:{sir}:\:{can}\:{you}\:{please}\:{crop}\:{the} \\ $$$${image}\:{properly}\:{when}\:{uploading}\:{it}? \\ $$ Commented by Rasheed.Sindhi…
Question Number 96784 by 175 last updated on 04/Jun/20 Answered by Sourav mridha last updated on 04/Jun/20 $$\:=\int\frac{\mathrm{2}+\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{2}} \sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{x}}+\mathrm{1}}}\:\boldsymbol{{dx}}\:+\frac{\mathrm{2}}{\boldsymbol{{x}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$=\int\frac{\boldsymbol{{d}}\left(\boldsymbol{{x}}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\:\sqrt{\left(\boldsymbol{{x}}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{2}} }}+\frac{\mathrm{2}}{\boldsymbol{{x}}}…
Question Number 162301 by mnjuly1970 last updated on 28/Dec/21 $$\: \\ $$$$\mathrm{lim}\:_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \:\left(\:\mathrm{1}−\:{sin}\left({x}\right)\right)^{\:\left(\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)−\mathrm{1}\:\right)} =? \\ $$$$ \\ $$ Answered by Mathspace last updated on 28/Dec/21…
Question Number 96771 by abdomathmax last updated on 04/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:+\mathrm{y}\:=\:\mathrm{cos}\left(\mathrm{2t}\right)\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$ Answered by mathmax by abdo last updated on 05/Jun/20 $$\mathrm{let}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{laplce}\:…
Question Number 162303 by mathlove last updated on 28/Dec/21 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{ln}^{\mathrm{2}} \left({x}+{y}+{z}\right){dxdydz}=? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 162297 by mathmax by abdo last updated on 28/Dec/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by Lordose last updated on 28/Dec/21 $$ \\…
Question Number 162299 by mathmax by abdo last updated on 28/Dec/21 $$\mathrm{calculta}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on…
Question Number 96763 by bobhans last updated on 04/Jun/20 $$\int\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:\mathrm{dx}}{\mathrm{cos}\:\mathrm{x}}\:=\:? \\ $$ Answered by Sourav mridha last updated on 04/Jun/20 $$=\int\frac{\mathrm{1}−\boldsymbol{{cosx}}}{\mathrm{2}\boldsymbol{{cos}}\left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)\boldsymbol{{cosx}}}\boldsymbol{{dx}} \\ $$$$=\int\frac{\boldsymbol{{sec}}^{\mathrm{2}} \frac{\boldsymbol{{x}}}{\mathrm{2}}}{\:\sqrt{\mathrm{1}−\boldsymbol{{tan}}^{\mathrm{2}} \frac{\boldsymbol{{x}}}{\mathrm{2}}}}\boldsymbol{{d}}\left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)−\int\boldsymbol{{sec}}\frac{\boldsymbol{{x}}}{\mathrm{2}}\boldsymbol{{d}}\left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)…