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Question-224642

Question Number 224642 by Rogerkeyter last updated on 23/Sep/25 Answered by som(math1967) last updated on 24/Sep/25 $$\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\frac{\boldsymbol{{e}}^{\sqrt{\mathrm{1}−\boldsymbol{{x}}}} }{\boldsymbol{{e}}^{\sqrt{\boldsymbol{{x}}}} }} \\ $$$$\:\:\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{e}}^{\sqrt{\boldsymbol{{x}}}}…

x-a-a-Z-0-a-Z-1-0-3-x-dx-

Question Number 224568 by fkwow344 last updated on 19/Sep/25 $$\sqrt{{x}}={a\begin{cases}{{a}\in\mathbb{Z}=\mathrm{0}}\\{{a}\notin\mathbb{Z}=\mathrm{1}}\end{cases}} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{3}} \:\sqrt{{x}}{dx}=? \\ $$ Commented by Ghisom_ last updated on 19/Sep/25 $$\mathrm{what}\:\mathrm{does}\:\mathrm{this}\:\mathrm{mean}? \\…

Question-224510

Question Number 224510 by Rogerkeyter last updated on 15/Sep/25 Answered by maths2 last updated on 16/Sep/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}}+\frac{{ln}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)}{\mathrm{1}−{x}}{dx} \\ $$$$=\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}}…