Question Number 37347 by math khazana by abdo last updated on 12/Jun/18 $${let}\:{r}\:=\sqrt{{p}^{\mathrm{2}} \:+{q}^{\mathrm{2}} }\:\:\:{p}\:{and}\:{q}\:{from}\:{R}\:\:{and}\:{p}>\mathrm{0}\:\:{q}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−{px}} \:\frac{{cos}\left({px}\right)}{\:\sqrt{{x}}}{dx}=\frac{\sqrt{\pi}}{{r}}\sqrt{\frac{{r}+{p}}{\mathrm{2}}} \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{px}} \:\:\frac{{sin}\left({qx}\right)}{\:\sqrt{{x}}}{dx}\:=\frac{\sqrt{\pi}}{{r}}\:\sqrt{\frac{{r}−{p}}{\mathrm{2}}}…
Question Number 37348 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\frac{{dt}}{{p}\:+{cost}}\:\:{with}\:{p}>\mathrm{1} \\ $$ Commented by prof Abdo imad last updated on…
Question Number 37346 by math khazana by abdo last updated on 12/Jun/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dt}}{{a}\:{cos}^{\mathrm{2}} {t}\:+{b}\:{sin}^{\mathrm{2}} {t}} \\ $$$${with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:. \\ $$ Terms of Service Privacy…
Question Number 37345 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:{I}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{\mathrm{1}+{acost}}{\mathrm{1}+\mathrm{2}{acost}\:+{a}^{\mathrm{2}} }{dt}\:\: \\ $$$$\left.\mathrm{1}\right)\:{if}\:\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{if}\:\mid{a}\mid>\mathrm{1} \\ $$ Terms of Service…
Question Number 37343 by math khazana by abdo last updated on 12/Jun/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{2}+{t}^{\mathrm{2}} \right){dt}\:. \\ $$…
Question Number 37338 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\:{B}_{{n}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:{sh}^{{n}} {xdx}\:. \\ $$ Commented by prof Abdo imad last…
Question Number 37337 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ch}^{{n}} {xdx}\:. \\ $$ Commented by math khazana by abdo…
Question Number 37317 by rahul 19 last updated on 11/Jun/18 $$\int\:\frac{\mathrm{acos}\:{x}+{b}}{\left({a}+{b}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:=\:? \\ $$ Commented by math khazana by abdo last updated on 12/Jun/18 $${changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)\:=\:{t}\:{give}\:…
Question Number 37316 by rahul 19 last updated on 11/Jun/18 $$\int\:\frac{{x}^{\mathrm{2}} }{\left({x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:=\:? \\ $$ Answered by ajfour last updated on 11/Jun/18 $${let}\:{x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\mathrm{sin}\:\left({x}+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}}\right)…
Question Number 37310 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)\left({x}^{\mathrm{2}} \:+\mathrm{9}\right)}\:. \\ $$ Commented by math khazana by…