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Category: Integration

Question-87556

Question Number 87556 by M±th+et£s last updated on 05/Apr/20 Commented by jagoll last updated on 05/Apr/20 $$\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{2}} +\mathrm{7x}−\mathrm{1}\:=\:\mathrm{a}\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} + \\ $$$$\mathrm{b}\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} +\mathrm{c}\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} \left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} +…

Question-87538

Question Number 87538 by Power last updated on 04/Apr/20 Commented by mathmax by abdo last updated on 04/Apr/20 $${I}\:=\int_{−\mathrm{1}} ^{\mathrm{1}} \:{f}^{−\mathrm{1}} \left({x}\right){dx}\:\:\:{changement}\:{f}^{−\mathrm{1}} \left({x}\right)={t}\:{give}\:{x}\:={f}\left({t}\right)\Rightarrow \\ $$$${dx}\:={f}^{'}…

Question-87540

Question Number 87540 by Power last updated on 04/Apr/20 Commented by abdomathmax last updated on 05/Apr/20 $${let}\:\:{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} }\:{changement}\:{x}\:={sh}\left({t}\right)\:{give} \\ $$$${I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ch}\left({t}\right)\:{dt}}{\left({sh}\left({t}\right)+{cht}\right)^{\mathrm{2}}…

Question-87511

Question Number 87511 by M±th+et£s last updated on 04/Apr/20 Answered by TANMAY PANACEA. last updated on 04/Apr/20 $${t}={x}^{\mathrm{3}} \rightarrow\frac{{dt}}{\mathrm{3}}={x}^{\mathrm{2}} {dx} \\ $$$$\int_{{ln}\mathrm{3}} ^{{ln}\mathrm{4}} \frac{\mathrm{1}}{\mathrm{3}}×\frac{{sint}}{{sint}+{sin}\left({ln}\mathrm{12}−{t}\right)}{dt}\:={I} \\…