Menu Close

Category: Integration

show-that-0-1-lnx-x-2-1-dx-2-8-

Question Number 210098 by klipto last updated on 30/Jul/24 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{lnx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}}\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{8}} \\ $$ Commented by AlagaIbile last updated on 30/Jul/24…

show-that-0-x-n-x-1-ax-b-dx-b-a-n-1-b-a-csc-n-a-gt-0-b-gt-0-n-lt-1-guys-kill-this-let-me-see-

Question Number 210112 by klipto last updated on 31/Jul/24 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} }{\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{ax}}+\boldsymbol{\mathrm{b}}\right)}\boldsymbol{\mathrm{dx}}=\frac{\left(\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}\right)^{\boldsymbol{\mathrm{n}}} −\mathrm{1}}{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{a}}}\boldsymbol{\pi\mathrm{csc}}\left(\boldsymbol{\pi\mathrm{n}}\right)\:\boldsymbol{\mathrm{a}}>\mathrm{0},\boldsymbol{\mathrm{b}}>\mathrm{0},\mid\boldsymbol{\mathrm{n}}\mid<\mathrm{1} \\ $$$$\boldsymbol{\mathrm{guys}}\:\boldsymbol{\mathrm{kill}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{let}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{see}} \\ $$ Answered by Spillover last updated…

6-0-2-5x-e-1-3-x-dx-

Question Number 210032 by klipto last updated on 29/Jul/24 $$\int_{\mathrm{6}} ^{\mathrm{0}} \left(\mathrm{2}+\mathrm{5}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{e}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\ $$ Answered by Sutrisno last updated on 29/Jul/24 $$=\int_{\mathrm{6}} ^{\mathrm{0}} \mathrm{2}{e}^{\frac{\mathrm{1}}{\mathrm{3}}{x}}…

prove-that-0-1-ln-1-t-tx-2-x-2-1-dx-sin-1-t-2-please-anyone-

Question Number 210082 by klipto last updated on 30/Jul/24 $$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{t}}+\boldsymbol{\mathrm{tx}}^{\mathrm{2}} \right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}}\mathrm{dx}=\left(\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \left(\sqrt{\boldsymbol{\mathrm{t}}}\right)\right)^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{anyone}}.. \\ $$ Answered by Frix last…

1-sin-2-x-1-cos-2-x-dx-

Question Number 209662 by depressiveshrek last updated on 18/Jul/24 $$\int\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}\right)}{dx} \\ $$ Answered by ARUNG_Brandon_MBU last updated on 18/Jul/24 $${I}=\int\frac{{dx}}{\mathrm{sin}^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}\right)} \\…