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Category: Integration

Question-73258

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}}…

let-0-lt-a-lt-1-calculate-0-ln-t-t-a-1-1-t-dt-and-0-ln-2-t-t-a-1-1-t-dt-

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…

calculate-A-n-0-1-x-n-2-x-2n-dx-and-J-n-0-2-x-3n-5-x-7n-dx-with-n-integr-natural-not-0-

Question Number 73230 by mathmax by abdo last updated on 08/Nov/19 $${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}+{x}^{{n}} }{\mathrm{2}+{x}^{\mathrm{2}{n}} }{dx}\:\:{and}\:{J}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{2}+{x}^{\mathrm{3}{n}} }{\mathrm{5}+{x}^{\mathrm{7}{n}} }{dx} \\ $$$${with}\:{n}\:{integr}\:{natural}\:{not}\:\mathrm{0} \\…

nice-calculus-evaluate-0-1-x-e-pi-1-x-e-1-ln-x-1-3-dx-3-pi-

Question Number 138742 by mnjuly1970 last updated on 17/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:……..\:{nice}\:\:\:….\:\:\:{calculus}… \\ $$$$\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{{e}^{\pi} −\mathrm{1}} −{x}^{{e}^{\gamma} −\mathrm{1}} }{{ln}\left(\sqrt[{\mathrm{3}}]{{x}}\:\right)}{dx}\overset{?} {=}\mathrm{3}\left(\pi−\gamma\right) \\ $$ Answered by…

2x-2-1-2x-x-2-1-x-2-x-x-1-x-2-1-dx-dx-x-x-1-1-x-3-

Question Number 73202 by MJS last updated on 08/Nov/19 $$\int\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}+\mathrm{2}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}^{\mathrm{2}} −{x}+\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx}=? \\ $$$$\int\frac{{dx}}{{x}\sqrt{{x}+\mathrm{1}}\sqrt{\left(\mathrm{1}−{x}\right)^{\mathrm{3}} }}=? \\ $$ Commented by mathmax by abdo last…