Question Number 30542 by abdo imad last updated on 23/Feb/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{{x}} \:\:{e}^{−{u}^{\mathrm{2}} } {du}=\:{x}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{e}^{−{x}^{\mathrm{2}} {tan}^{\mathrm{2}} {t}} }{{cos}^{\mathrm{2}} {t}}{dt}\:\:. \\ $$$$ \\ $$…
Question Number 161609 by amin96 last updated on 20/Dec/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{xln}}\left(\mathrm{1}+\boldsymbol{{x}}^{\mathrm{4}} \right)}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30527 by abdo imad last updated on 22/Feb/18 $${find}\:\:{I}_{{n},{p}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{x}^{{n}} \:{e}^{−{px}} \:\:\:\:\:{with}\:{n}\:{and}\:{p}\:{from}\:{N}^{\bigstar} \:. \\ $$ Answered by sma3l2996 last updated on…
Question Number 30525 by abdo imad last updated on 22/Feb/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{x}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{give}\:{I}\:{at}\:{form}\:{of}\:{series}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30521 by abdo imad last updated on 22/Feb/18 $$\left.\mathrm{1}\right)\:{find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{{n}} \:{cos}\left({narctanx}\right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\right)^{\mathrm{3}} \:{cos}\left(\mathrm{3}\:{arctanx}\right){dx}\:. \\ $$ Commented by…
Question Number 30518 by abdo imad last updated on 22/Feb/18 $${let}\:{a}>\mathrm{0}\:{find}\:\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}+{a}\right)\sqrt{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }}\:. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $${f}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 30512 by abdo imad last updated on 22/Feb/18 $${find}\:\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\sqrt{\frac{\mathrm{1}−{t}}{\mathrm{1}+{t}}}\:{dt}\:. \\ $$ Commented by abdo imad last updated on 24/Feb/18 $${the}\:{ch}.{t}={cos}\theta\:{give}\:{I}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 30507 by abdo imad last updated on 22/Feb/18 $${find}\:\int_{−\pi} ^{\pi} \:\:\frac{{dx}}{\mathrm{2}+{cosx}} \\ $$$$\left.\mathrm{2}\right)\:{if}\:\:\frac{\mathrm{1}}{\mathrm{2}+{cosx}}=\:\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}\geqslant\mathrm{1}} {a}_{{n}} \:{cos}\left({nx}\right)\:\:{find}\:{a}_{\mathrm{0}} \:{and}\:{a}_{{n}} \:. \\ $$ Terms of Service…
Question Number 30508 by abdo imad last updated on 22/Feb/18 $${find}\:{I}=\:\int\:\:{e}^{{arcsinx}} {dx}\:. \\ $$ Commented by sma3l2996 last updated on 24/Feb/18 $${I}=\int{e}^{{arcsinx}} {dx} \\ $$$${u}={e}^{{arcsinx}}…
Question Number 30506 by abdo imad last updated on 22/Feb/18 $${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{{x}} \:\:\:\frac{{t}}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}\:{with}\:{x}>\mathrm{0}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com