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Category: Integration

Question-65729

Question Number 65729 by aliesam last updated on 02/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $$\left.{a}\right)\:\:{let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:{e}^{{ix}} \:{x}^{−\alpha} \:{dx}\:\:\Rightarrow{f}\left(\alpha\right)\:=_{{ix}\:={t}} \:\:\:\int_{\mathrm{0}} ^{\infty}…

1-dx-1-sin-x-cos-x-2-0-x-x-3-1-dx-3-0-1-x-3-2-1-dx-

Question Number 131247 by bramlexs22 last updated on 03/Feb/21 $$\left(\mathrm{1}\right)\:\psi\:=\:\int\:\frac{{dx}}{\mathrm{1}−\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}=? \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}}{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}\:=? \\ $$$$\left(\mathrm{3}\right)\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{3}/\mathrm{2}} +\mathrm{1}}\:{dx}\:=?\: \\ $$ Answered by liberty…

ln-2-xsin-x-dx-

Question Number 65704 by mmkkmm000m last updated on 03/Aug/19 $$\int{ln}^{\mathrm{2}} {xsin}\left({x}\right){dx} \\ $$ Commented by Tinku Tara last updated on 02/Aug/19 $$\mathrm{Can}\:\mathrm{please}\:\mathrm{use}\:\mathrm{smaller}\:\mathrm{font}\:\mathrm{size} \\ $$ Terms…

evaluate-f-a-b-a-b-b-x-x-a-dx-

Question Number 164 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:{f}\left({a},{b}\right)=\underset{{a}} {\overset{{b}} {\int}}\left({b}−{x}\right)\left({x}−{a}\right){dx} \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\left({b}−{x}\right)\left({x}−{a}\right)=−{x}^{\mathrm{2}} +\left({a}+{b}\right){x}−{ab} \\…

real-analysis-prove-0-1-ln-ln-1-x-ln-2-x-dx-3-2-

Question Number 131227 by mnjuly1970 last updated on 02/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{real}\:\:{analysis}\:… \\ $$$$\:\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\boldsymbol{\Omega}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({ln}\left(\frac{\mathrm{1}}{{x}}\right)\right){ln}^{\mathrm{2}} \left({x}\right){dx}=\mathrm{3}−\mathrm{2}\gamma \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…