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Question-201351

Question Number 201351 by sonukgindia last updated on 05/Dec/23 Answered by Sutrisno last updated on 05/Dec/23 $$=\int_{\mathrm{0}} ^{\pi} \frac{{x}}{\mathrm{1}+{sinx}}.\frac{\mathrm{1}−{sinx}}{\mathrm{1}−{sinx}}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\pi} \frac{{x}−{xsinx}}{\mathrm{1}−{sin}^{\mathrm{2}} {x}}{dx} \\…

Question-201411

Question Number 201411 by MrGHK last updated on 05/Dec/23 Commented by mr W last updated on 06/Dec/23 $${Mr}\:{Laplac}:\:{please}\:{post}\:{your}\:{answer} \\ $$$${in}\:{the}\:{thread}\:{corresponding}\:{to}\:{the} \\ $$$${question}!\:{otherwise}\:{it}'{s}\:{not}\:{clear} \\ $$$${what}\:{your}\:{post}\:{is}\:{for}. \\…

Question-201329

Question Number 201329 by MrGHK last updated on 04/Dec/23 Answered by witcher3 last updated on 04/Dec/23 $$=\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{2n}+\mathrm{1}}\underset{\mathrm{m}\geqslant\mathrm{0}} {\sum}\left(−\mathrm{1}\right)^{\mathrm{m}} \int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{m}+\mathrm{2n}+\mathrm{1}} \mathrm{dx} \\…

Question-201292

Question Number 201292 by sonukgindia last updated on 03/Dec/23 Answered by aleks041103 last updated on 03/Dec/23 $${I}=\underset{−{a}} {\overset{{a}} {\int}}\frac{{cos}\left({x}\right){dx}}{\mathrm{1}+{e}^{\pi/{x}} }=\underset{{a}} {\overset{−{a}} {\int}}\frac{{cos}\left(−{x}\right){d}\left(−{x}\right)}{\mathrm{1}+{e}^{\pi/\left(−{x}\right)} }= \\ $$$$=\int_{−{a}}…

Question-201293

Question Number 201293 by sonukgindia last updated on 03/Dec/23 Answered by aleks041103 last updated on 03/Dec/23 $${I}=\int_{\mathrm{2}} ^{\:\infty} \frac{\mathrm{8}{arcsec}\left({x}/\mathrm{2}\right){dx}}{{x}^{\mathrm{3}} −\mathrm{4}{x}}= \\ $$$$=\int_{\mathrm{1}} ^{\:\infty} \frac{\mathrm{8}{arcsec}\left(\left(\mathrm{2}{x}\right)/\mathrm{2}\right)}{\left(\mathrm{2}{x}\right)^{\mathrm{3}} −\mathrm{4}\left(\mathrm{2}{x}\right)}{d}\left(\mathrm{2}{x}\right)=\mathrm{2}\int_{\mathrm{1}}…

Question-201290

Question Number 201290 by sonukgindia last updated on 03/Dec/23 Answered by Calculusboy last updated on 03/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{By}}\:\boldsymbol{{using}}\:\boldsymbol{{kings}}\:\boldsymbol{{rule}} \\ $$$$\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\boldsymbol{{sin}}^{\boldsymbol{\varphi}} \left(\boldsymbol{{x}}\right)}{\boldsymbol{{sin}}^{\boldsymbol{\varphi}} \left(\boldsymbol{{x}}\right)+\boldsymbol{{cos}}^{\boldsymbol{\varphi}} \left(\boldsymbol{{x}}\right)}\boldsymbol{{dx}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}}…