Question Number 219682 by Nicholas666 last updated on 30/Apr/25 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{log}\left(\mathrm{1}+{x}\right)\centerdot\mathrm{Li}_{{s}} \left({x}\right)}{{x}\centerdot\zeta\left({s}+\mathrm{1},{x}\right)}\:{dx} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 219634 by Nicholas666 last updated on 29/Apr/25 Answered by MrGaster last updated on 01/May/25
Question Number 219620 by Nicholas666 last updated on 29/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{Prove};\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{50}{x}^{\mathrm{8}} }{{x}^{\mathrm{20}} +\mathrm{2}{x}^{\mathrm{10}} +\mathrm{1}}\:{dx}\:=\:\phi\pi \\ $$$$ \\ $$ Answered by…
Question Number 219618 by Nicholas666 last updated on 29/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:{Prove}; \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{{ln}\:{ln}\:\frac{\mathrm{1}}{{x}}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }\:{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left({ln}\left(\frac{\pi}{\mathrm{2}}\right)−\gamma\right) \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 219619 by Nicholas666 last updated on 29/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \left({x}^{\mathrm{2}} +\mathrm{1}\right)^{−\mathrm{1}/\mathrm{2}} {dx} \\ $$$$ \\ $$ Answered by Ghisom last updated…
Question Number 219600 by Nicholas666 last updated on 29/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{1}} ^{\:\mathrm{2}} \left[{x}\right]^{{x}} \:{dx} \\ $$$$ \\ $$ Answered by Nicholas666 last updated on…
Question Number 219586 by Hery03 last updated on 29/Apr/25 $${Integrate}\:: \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{2}} \:−\:{x}}\:+\:\mathrm{1}}{dx}. \\ $$ Answered by Ghisom last updated on 29/Apr/25 $$\int\frac{{x}^{\mathrm{2}} }{\:\mathrm{1}+\sqrt{{x}}\sqrt{{x}−\mathrm{1}}}{dx}=…
Question Number 219550 by Spillover last updated on 28/Apr/25 Answered by Nicholas666 last updated on 29/Apr/25 $${I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{7}} \right){ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right){lnx}}{dx}\:\:\:\:\:\:\: \\ $$$${I}\left({a}\right)=\int_{\mathrm{0}} ^{\:\infty}…
Question Number 219549 by Spillover last updated on 28/Apr/25 Answered by Nicholas666 last updated on 29/Apr/25 $$\int\frac{\mathrm{1}+{sin}\:{x}}{\mathrm{1}−{sinx}}{dx}=\mathrm{2}{tany}−{x}+{c} \\ $$$$\int\frac{\left(\mathrm{1}+{sin}\:{x}\right)^{\mathrm{2}} }{\mathrm{1}−{sin}^{\mathrm{2}} {x}}{dx}=\mathrm{2}\:{tan}\:{y}\:−{x}\:+{c} \\ $$$$\int\frac{\mathrm{1}+\mathrm{2}\:{sin}\:{x}+{sin}^{\mathrm{2}} {x}}{{cos}^{\mathrm{2}} {x}}{dx}=\mathrm{2}\:{tan}\:{y}\:−{x}+{c}…
Question Number 219552 by Nicholas666 last updated on 28/Apr/25 Answered by mr W last updated on 29/Apr/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}_{{k}} ^{\alpha} \mathrm{ln}\:\left({x}_{{k}} \right){dx}_{{k}} \\ $$$$=\frac{\mathrm{1}}{\alpha+\mathrm{1}}\int_{\mathrm{0}}…