Menu Close

Author: Tinku Tara

I-0-1-ln-x-1-x-2-1-dx-

Question Number 223933 by MathematicalUser2357 last updated on 10/Aug/25 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left({x}+\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Answered by Tawa11 last updated on 10/Aug/25 $$\mathrm{Note}:\:\:\:\:\mathrm{I}\left(\mathrm{a}\right)\:\:=\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{a}} \:\frac{\mathrm{ln}\left(\mathrm{1}\:\:+\:\:\mathrm{ax}\right)}{\mathrm{1}\:\:+\:\:\mathrm{x}^{\mathrm{2}}…

Question-223928

Question Number 223928 by mr W last updated on 09/Aug/25 Commented by mr W last updated on 14/Aug/25 $${a}\:{mass}\:\boldsymbol{{m}}\:{is}\:{tied}\:{on}\:{each}\:{end}\:{of}\: \\ $$$${an}\:{uniform}\:{rope}\:{with}\:{mass}\:\boldsymbol{{M}}\: \\ $$$${and}\:{length}\:\boldsymbol{{L}}.\:{in}\:{how}\:{many}\:{ways} \\ $$$${can}\:{the}\:{rope}\:{be}\:{supported}\:{on}\:{the}…

Question-223908

Question Number 223908 by yerlow3 last updated on 09/Aug/25 Answered by dionigi last updated on 10/Aug/25 $$ \\ $$$${ABCD}\:{should}\:{be}\:{a}\:{regular}\:{hemi}−{hexagon} \\ $$$${r}\:=\:{PA}\:=\:{PB}\:=\:{PC}\:=\:{PD} \\ $$$${r}\:=\:{DA}\:=\:{AB}\:=\:{BC} \\ $$$${and}\:{P}\:{the}\:{center}\:{of}\:{thr}\:{circle}…