Question Number 38458 by maxmathsup by imad last updated on 25/Jun/18 $${let}\:\mid{x}\mid<\mathrm{1}\:\:{calculate}\:\:{F}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right){dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}\:+\frac{\mathrm{1}}{\mathrm{2}}{t}^{\mathrm{2}} \right){dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{sin}\theta\:{t}^{\mathrm{2}} \right){dt}\:.…
Question Number 38454 by maxmathsup by imad last updated on 25/Jun/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}−{cos}\left({xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }\:{e}^{−{xt}^{\mathrm{2}} } {dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}−{cos}\left(\mathrm{2}{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}}…
Question Number 38453 by maxmathsup by imad last updated on 25/Jun/18 $${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}−{cos}\left({xt}\right)}{{t}}\:{e}^{−{xt}} {dt}\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{asimple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}−{cos}\left(\pi{t}\right)}{{t}}\:{e}^{−{t}} {dt} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\infty}…
Question Number 38451 by MJS last updated on 25/Jun/18 $$\mathrm{new}\:\mathrm{attempt}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{qu}.\:\mathrm{37630} \\ $$$$ \\ $$$$\int\frac{{dx}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}}= \\ $$$$\:\:\:\:\:\left[{t}={x}+\mathrm{1}\:\rightarrow\:{dx}={dt}\right] \\ $$$$=\int\frac{{dt}}{\:\sqrt{{t}−\mathrm{1}}+\sqrt{{t}}+\sqrt{{t}+\mathrm{1}}}= \\ $$$$ \\ $$$$\:\:\:\:\:\begin{bmatrix}{\mathrm{to}\:\mathrm{omit}\:\mathrm{the}\:\mathrm{roots}}\\{\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}\:\mathrm{must}\:\mathrm{be}\:\mathrm{multiplied}\:\mathrm{with}}\\{\left(−\sqrt{{a}}−\sqrt{{b}}+\sqrt{{c}}\right)\left(−\sqrt{{a}}+\sqrt{{b}}−\sqrt{{c}}\right)\left(\sqrt{{a}}−\sqrt{{b}}−\sqrt{{c}}\right)}\\{\frac{\mathrm{1}}{\:\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}}=\frac{{a}^{\mathrm{3}/\mathrm{2}} +{b}^{\mathrm{3}/\mathrm{2}} +{c}^{\mathrm{3}/\mathrm{2}} +\mathrm{2}\sqrt{{abc}}−\left(\left({a}+{b}\right)\sqrt{{c}}+\left({a}+{c}\right)\sqrt{{b}}+\left({b}+{c}\right)\sqrt{{a}}\right)}{{a}^{\mathrm{2}}…
Question Number 103974 by abdomsup last updated on 18/Jul/20 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} } \\ $$ Answered by OlafThorendsen last updated on 18/Jul/20 $$\mathrm{R}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}}…
Question Number 169504 by bagjagugum123 last updated on 01/May/22 Commented by bagjagugum123 last updated on 01/May/22 $${Prove}\:{that} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 38397 by Fawomath last updated on 25/Jun/18 $${evaluate}\:\:\int{secxdx} \\ $$ Commented by maxmathsup by imad last updated on 25/Jun/18 $${let}\:{I}=\:\int\:\:\:\frac{{dx}}{{cosx}}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${I}=\:\:\int\:\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 38405 by malwaan last updated on 25/Jun/18 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{3}\right)=\mathrm{3};\mathrm{f}\left(\mathrm{1}\right)=\mathrm{2}\: \\ $$$$\Rightarrow\int_{\mathrm{1}} ^{\mathrm{3}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{f}^{'} \left(\mathrm{x}\right)\mathrm{dx}=….. \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 25/Jun/18 $${pls}\:{clarify}\:\left[\left({x}\right)\right]\:{is}\:{it}\:{floor}/{greatest}\:{integer}…
Question Number 38384 by NECx last updated on 24/Jun/18 $$\int{x}^{−\mathrm{3}{cosx}} {dx} \\ $$$$ \\ $$$${please}\:{is}\:{this}\:{possible}? \\ $$$${If}\:{possibld}\:{then}\:{prove}\:{it}. \\ $$$$ \\ $$$${Thanks}\:{in}\:{advance}. \\ $$ Commented by…
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