Question Number 97091 by Mathudent last updated on 06/Jun/20 $${solve}\:\int{x}^{{x}+\mathrm{1}} {dx}\:. \\ $$ Answered by Sourav mridha last updated on 06/Jun/20 $$\int\boldsymbol{{e}}^{\left(\boldsymbol{{x}}+\mathrm{1}\right).\boldsymbol{{l}}\mathrm{n}\left(\boldsymbol{{x}}\right)} \boldsymbol{{dx}} \\ $$$$=\int\underset{\boldsymbol{{n}}=\mathrm{0}}…
Question Number 97089 by Mathudent last updated on 06/Jun/20 $${solve}\:\:\int{x}^{{x}} \left(\mathrm{1}+\mathrm{ln}\:{x}\right){dx}\:. \\ $$ Answered by M±th+et+s last updated on 06/Jun/20 $${let}\:{x}^{{x}} ={u}\:\:\:\:{du}={x}^{{x}} \left(\mathrm{1}+{ln}\left({x}\right)\right){dx} \\ $$$$\int{du}={u}+{c}…
Question Number 97082 by bobhans last updated on 06/Jun/20 Answered by john santu last updated on 06/Jun/20 Commented by bobhans last updated on 06/Jun/20 $$\mathrm{thank}\:\mathrm{you}…
Question Number 162604 by amin96 last updated on 30/Dec/21 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \boldsymbol{{xtg}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}=? \\ $$ Answered by Ar Brandon last updated on 30/Dec/21 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {x}\mathrm{tan}{xdx}…
Question Number 97059 by mhmd last updated on 06/Jun/20 Commented by PRITHWISH SEN 2 last updated on 06/Jun/20 $$\mathrm{let}\: \\ $$$$\:\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{sin}^{−\mathrm{1}} \mathrm{x}−\mathrm{1}}\:=\:\mathrm{v}\left(\mathrm{x}\right) \\ $$$$\mathrm{then}\:\mathrm{v}^{'}…
Question Number 97057 by bemath last updated on 06/Jun/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{−\mathrm{ln}\left({x}\right)}}\:?\:\left[\:{by}\:{G}\mathrm{amma}\:\mathrm{function}\:\right] \\ $$ Answered by Sourav mridha last updated on 06/Jun/20 $$\boldsymbol{{let}}\:\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right)=−\boldsymbol{{k}}.. \\ $$$$=\int_{\mathrm{0}}…
Question Number 31517 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}}\:\:. \\ $$ Commented by abdo imad last updated on 12/Mar/18 $${let}\:{put}\:{I}\left(\xi\right)\:=\int_{−\mathrm{1}+\xi} ^{\mathrm{1}+\xi}…
Question Number 31516 by abdo imad last updated on 09/Mar/18 $${find}\:\int\:\:\:\frac{{dx}}{{x}\:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on 16/Mar/18 $${I}\:=\:\int\:\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:−{x}\right){dx}=\:\int\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:{dx}\:−\frac{{x}^{\mathrm{2}}…
Question Number 31515 by abdo imad last updated on 09/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{{chx}}\:. \\ $$ Commented by abdo imad last updated on 10/Mar/18 $${I}=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 31514 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }{dx}. \\ $$ Answered by sma3l2996 last updated on 10/Mar/18 $${by}\:{parts}\: \\…