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Author: Tinku Tara

Question-200861

Question Number 200861 by sonukgindia last updated on 25/Nov/23 Answered by Mathspace last updated on 25/Nov/23 $${J}=_{{x}={t}^{\frac{\mathrm{1}}{\mathrm{10}}} } \frac{\mathrm{1}}{\mathrm{10}}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{5}}{\mathrm{1}+{t}}{t}^{\frac{\mathrm{1}}{\mathrm{10}}−\mathrm{1}} {dt} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\infty}…

Question-200862

Question Number 200862 by sonukgindia last updated on 25/Nov/23 Answered by Mathspace last updated on 25/Nov/23 $$\Phi \\ $$$$=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{5}{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{10}} }{dx}=_{{x}={t}^{\frac{\mathrm{1}}{\mathrm{10}}} } \frac{\mathrm{1}}{\mathrm{10}}\int_{\mathrm{0}}…

Question-200863

Question Number 200863 by sonukgindia last updated on 25/Nov/23 Answered by Mathspace last updated on 25/Nov/23 $${x}^{\mathrm{2}\pi} ={t}\:\Rightarrow{x}={t}^{\frac{\mathrm{1}}{\mathrm{2}\pi}} \:{and} \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\frac{\pi}{\mathrm{5}}−\mathrm{1}} }{\mathrm{1}+{x}^{\mathrm{2}\pi} }{dx}=\frac{\mathrm{1}}{\mathrm{2}\pi}\int_{\mathrm{0}}…