Question Number 73293 by ~blr237~ last updated on 10/Nov/19 $${Explicit}\:\:{f}\left({x}\right)=\:\int_{\mathrm{1}} ^{\infty} \:\frac{{lnt}}{\left({x}^{\mathrm{2}} +{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dt}\: \\ $$ Commented by mathmax by abdo last updated on…
Question Number 138819 by qaz last updated on 18/Apr/21 $$\left(\mathrm{1}\right)::{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \mid{x}−\mathrm{2}{t}\mid{dt},\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{3}} {f}\left({x}\right){dx}=? \\ $$$$−−−−−−−−−−−−−−−−−−− \\ $$$$\left(\mathrm{2}\right)::{f}\left({x}\right)={x}^{\mathrm{2}} \centerdot\int_{\mathrm{1}} ^{{x}} \frac{{dt}}{{t}^{\mathrm{3}} −\mathrm{3}{t}^{\mathrm{2}} +\mathrm{3}{t}},\:\:\:\:\:\:\:\:\:\:\:\:\:{f}^{\left(\mathrm{2019}\right)} \left(\mathrm{1}\right)=? \\…
Question Number 73279 by byaw last updated on 09/Nov/19 Answered by mr W last updated on 09/Nov/19 $$\mathrm{40}={v}_{\mathrm{0}} ×\mathrm{4}+\frac{\mathrm{1}}{\mathrm{2}}{a}×\mathrm{4}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{10}={v}_{\mathrm{0}} +\mathrm{2}{a}\:\:\:…\left({i}\right) \\ $$$$\mathrm{72}={v}_{\mathrm{0}} ×\mathrm{6}+\frac{\mathrm{1}}{\mathrm{2}}{a}×\mathrm{6}^{\mathrm{2}}…
Question Number 73275 by solihin last updated on 09/Nov/19 $$ \\ $$$$ \\ $$$$\int\frac{\mathrm{4}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}−{x}\delta\varkappa}}\:\:\:\:? \\ $$$$ \\ $$ Commented by MJS last updated on…
Question Number 138810 by mathdanisur last updated on 18/Apr/21 $$\underset{\:\mathrm{0}} {\overset{\:\pi/\mathrm{2}} {\int}}\frac{{xsin}\left({x}\right)}{\mathrm{1}−{cosx}}\centerdot{log}\left(\mathrm{1}+{cosx}\right){dx}=? \\ $$ Answered by phanphuoc last updated on 18/Apr/21 $${u}={x},{dv}={ln}\left(\mathrm{1}+{cosx}\right){dcosx}/\left(\mathrm{1}−{cosx}\right) \\ $$ Commented…
Question Number 138801 by mnjuly1970 last updated on 18/Apr/21 $$\: \\ $$$$\:\:\:\:\:\:\:{lim}_{\:{n}\rightarrow\infty} \left(\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left(\mathrm{1}−{x}\right)^{{n}} {e}^{{x}} }{{n}!}{dx}\right)=? \\ $$ Answered by Kamel last updated on…
Question Number 138799 by TheSupreme last updated on 18/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{tan}\left(\mathrm{x}\right)−\alpha\right){dx}=… \\ $$$$\alpha\in\mathbb{C} \\ $$ Answered by mathmax by abdo last updated on 19/Apr/21…
Question Number 73258 by Lontum Hans last updated on 09/Nov/19 Answered by MJS last updated on 09/Nov/19 $$\mathrm{well},\:\mathrm{just}\:\mathrm{do}\:\mathrm{it} \\ $$$${u}=\mathrm{1}+\mathrm{cosh}\:{x}\:\rightarrow\:{dx}=\frac{{du}}{\mathrm{sinh}\:{x}} \\ $$$$…=\underset{\mathrm{2}} {\overset{\mathrm{3}} {\int}}\frac{{du}}{{u}\left({u}−\mathrm{1}\right)}=\left[\mathrm{ln}\:\frac{{u}−\mathrm{1}}{{u}}\right]_{\mathrm{2}} ^{\mathrm{3}}…
Question Number 73238 by mathmax by abdo last updated on 08/Nov/19 $${let}\:\mathrm{0}<{a}<\mathrm{1}\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({t}\right){t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}^{\mathrm{2}} \left({t}\right){t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt} \\ $$ Commented by mathmax by…
Question Number 138771 by qaz last updated on 18/Apr/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {ln}\:\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx}=? \\ $$ Answered by Kamel last updated on 19/Apr/21 Answered by…