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 $$\mathrm{Note}:\:\:\:\:\mathrm{I}\left(\mathrm{a}\right)\:\:=\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{a}} \:\frac{\mathrm{ln}\left(\mathrm{1}\:\:+\:\:\mathrm{ax}\right)}{\mathrm{1}\:\:+\:\:\mathrm{x}^{\mathrm{2}}…
Question Number 223935 by fantastic last updated on 10/Aug/25 Commented by fantastic last updated on 10/Aug/25 $${PERIMETER} \\ $$ Answered by dionigi last updated on…
Question Number 223954 by MASANJAJJ last updated on 10/Aug/25 Answered by som(math1967) last updated on 11/Aug/25 $$\:{x}=\angle{BDC} \\ $$$$\angle{DBA}=\angle{BCD} \\ $$$$\:\therefore{x}=\mathrm{10}+\mathrm{90}−{x}\Rightarrow{x}=\mathrm{50} \\ $$ Answered by…
Question Number 223917 by tun26114 last updated on 09/Aug/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 223928 by mr W last updated on 09/Aug/25 Commented by mr W last updated on 14/Aug/25 $${a}\:{mass}\:\boldsymbol{{m}}\:{is}\:{tied}\:{on}\:{each}\:{end}\:{of}\: \\ $$$${an}\:{uniform}\:{rope}\:{with}\:{mass}\:\boldsymbol{{M}}\: \\ $$$${and}\:{length}\:\boldsymbol{{L}}.\:{in}\:{how}\:{many}\:{ways} \\ $$$${can}\:{the}\:{rope}\:{be}\:{supported}\:{on}\:{the}…
Question Number 223908 by yerlow3 last updated on 09/Aug/25 Answered by dionigi last updated on 10/Aug/25 $$ \\ $$$${ABCD}\:{should}\:{be}\:{a}\:{regular}\:{hemi}−{hexagon} \\ $$$${r}\:=\:{PA}\:=\:{PB}\:=\:{PC}\:=\:{PD} \\ $$$${r}\:=\:{DA}\:=\:{AB}\:=\:{BC} \\ $$$${and}\:{P}\:{the}\:{center}\:{of}\:{thr}\:{circle}…
Question Number 223920 by Mathspace last updated on 09/Aug/25 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}} }{{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by Frix last updated on 09/Aug/25 $$\mathrm{by}\:\mathrm{parts}\:\left(\mathrm{2}\:\mathrm{times}\right) \\…
Question Number 223905 by TonyCWX last updated on 09/Aug/25 $${ABCD}\:{is}\:{a}\:{square} \\ $$$${EL}={LF} \\ $$$${FN}={ND} \\ $$$${O}\:{is}\:{the}\:{center}\:{of}\:{square} \\ $$$${Prove}\:{that}\:{points}\:{K},\:{L},\:{O},\:{N}\:{and}\:{C}\:{are}\:{concyclic} \\ $$ Commented by TonyCWX last updated…
Question Number 223923 by Mathspace last updated on 09/Aug/25 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$ Answered by Tawa11 last updated on 14/Aug/25 $$\:\mathrm{Finally}:\: \\ $$$$\:\:\:\:\int_{\:\mathrm{0}}…
Question Number 223901 by mr W last updated on 08/Aug/25 Commented by mr W last updated on 08/Aug/25 $${find}\:{the}\:{area}\:{of}\:{circle}. \\ $$ Commented by Hamada1969 last…