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Category: Integration

sin-ln3x-dx-

Question Number 106807 by Study last updated on 07/Aug/20 $$\int{sin}\left({ln}\mathrm{3}{x}\right){dx}=??? \\ $$ Answered by bemath last updated on 08/Aug/20 $$\:\:\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\mathrm{ln}\:\mathrm{3x}=\mathrm{u}\:\Rightarrow\mathrm{3x}=\mathrm{e}^{\mathrm{u}} \:;\:\mathrm{dx}\:=\:\frac{\mathrm{e}^{\mathrm{u}} \:\mathrm{du}}{\mathrm{3}} \\…

Question-41248

Question Number 41248 by Tawa1 last updated on 04/Aug/18 Commented by prof Abdo imad last updated on 04/Aug/18 $${changement}\:{x}=\sqrt{\mathrm{2}}{tant}\:\Rightarrow \\ $$$${I}\:=\:\int\:\:\frac{\sqrt{\mathrm{2}}\left(\mathrm{1}+{tan}^{\mathrm{2}} {t}\right){dt}}{\mathrm{8}\left(\mathrm{1}+{tan}^{\mathrm{2}} {t}\right)^{\mathrm{3}} }\:=\frac{\sqrt{\mathrm{2}}}{\mathrm{8}}\:\int\:\:\:\frac{{dt}}{\left(\mathrm{1}+{tan}^{\mathrm{2}} {t}\right)^{\mathrm{2}}…

Question-41246

Question Number 41246 by Raj Singh last updated on 04/Aug/18 Commented by prof Abdo imad last updated on 04/Aug/18 $${let}\:{A}\:=\:\int\:\:\:\:\frac{{sin}\left({lnx}\right)}{{x}^{\mathrm{3}} }{dx}\:{changement}\:{ln}\left({x}\right)={t} \\ $$$${give}\:{A}\:=\int\:\:\frac{{sin}\left({t}\right)}{{e}^{\mathrm{3}{t}} }\:{e}^{{t}} {dt}=\:\int\:\:{e}^{−\mathrm{2}{t}}…

determine-using-laplce-transformation-this-integrale-0-tsin-tx-a-2-t-2-dt-

Question Number 106691 by Laplace last updated on 06/Aug/20 $$\boldsymbol{{determine}}\:\boldsymbol{{using}}\:\:\boldsymbol{{laplce}}\:\boldsymbol{{transformation}}\:\boldsymbol{{this}} \\ $$$$\boldsymbol{{integrale}}\: \\ $$$$\:\:\int_{\mathrm{0}} ^{+\infty} \frac{\boldsymbol{{tsin}}\left(\boldsymbol{{tx}}\right)}{\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{t}}^{\mathrm{2}\:} }\boldsymbol{{dt}} \\ $$ Answered by mathmax by abdo…