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Category: Integration

Question-65740

Question Number 65740 by rajesh4661kumar@gmail.com last updated on 03/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 letA=dx1cosx+sinxA=cosx1+cosxsinxdxchangement$${tan}\left(\frac{{x}}{\mathrm{2}\:}\right)\:={t}\:{give}\:{A}\:=\int\:\:\:\frac{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{1}+\frac{\mathrm{2}{t}\left(\mathrm{1}−{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}}…

Question-65729

Question Number 65729 by aliesam last updated on 02/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $$\left.{a}\right)\:\:{let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:{e}^{{ix}} \:{x}^{−\alpha} \:{dx}\:\:\Rightarrow{f}\left(\alpha\right)\:=_{{ix}\:={t}} \:\:\:\int_{\mathrm{0}} ^{\infty}…