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Category: Integration

let-f-x-0-pi-2-d-x-cos-2-with-x-gt-0-1-calculate-f-x-and-f-x-2-find-f-n-x-and-f-n-0-3-developp-f-at-integr-serie-

Question Number 40619 by math khazana by abdo last updated on 25/Jul/18 $${let}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{d}\theta}{{x}\:\:+{cos}^{\mathrm{2}} \theta}\:\:{with}\:{x}>\mathrm{0}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right)\:{and}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}.…

find-x-1-1-x-2-1-x-2-x-1-dx-

Question Number 40620 by math khazana by abdo last updated on 25/Jul/18 $${find}\:\:\int\:\:\:\left(\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jul/18 $$\int{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…

question-106075-again-1-cosx-99cosx-70sinx-210-cosx-66sinx-110-dx-using-t-tan-x-2-I-get-4-dt-t-4-8t-3-22t-2-272t-419-can-someone-factorize-the-denominator-

Question Number 106120 by Her_Majesty last updated on 02/Aug/20 $${question}\:\mathrm{106075}\:{again} \\ $$$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$$${using}\:{t}={tan}\left({x}/\mathrm{2}\right)\:{I}\:{get} \\ $$$$−\mathrm{4}\int\frac{{dt}}{{t}^{\mathrm{4}} +\mathrm{8}{t}^{\mathrm{3}} −\mathrm{22}{t}^{\mathrm{2}} +\mathrm{272}{t}−\mathrm{419}} \\ $$$${can}\:{someone}\:{factorize}\:{the}\:{denominator}? \\ $$ Commented by…