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Category: Integration

I-1-e-dx-x-1-ln-2-x-

Question Number 65372 by aliesam last updated on 29/Jul/19 $${I}=\int_{\mathrm{1}} ^{{e}} \:\frac{{dx}}{{x}\left(\mathrm{1}+{ln}^{\mathrm{2}} {x}\right)} \\ $$ Commented by Prithwish sen last updated on 29/Jul/19 $$\mathrm{put}\:\mathrm{lnx}=\mathrm{tan}\theta\Rightarrow\frac{\mathrm{dx}}{\mathrm{x}}=\mathrm{sec}^{\mathrm{2}} \theta\mathrm{d}\theta…

find-dx-x-1-x-2-x-3-

Question Number 65355 by mathmax by abdo last updated on 28/Jul/19 $${find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)}} \\ $$ Commented by Prithwish sen last updated on 29/Jul/19 $$\int\frac{\mathrm{dx}}{\:\sqrt{\left\{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{1}\right\}\left(\mathrm{x}+\mathrm{2}\right)}}\:\:\:\mathrm{putting}\:\left(\mathrm{x}+\mathrm{2}\right)=\mathrm{a} \\…

Question-65332

Question Number 65332 by aliesam last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 29/Jul/19 $${let}\:{suppose}\:{n}\:{inter}\:{let}\:{decompose}\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\frac{{x}}{{x}^{{n}} \:+\mathrm{1}} \\ $$$${z}^{{n}} \:+\mathrm{1}\:=\mathrm{0}\:\Rightarrow{z}^{{n}}…

Question-65320

Question Number 65320 by hovea cw last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 28/Jul/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}}{lnxdx}\:{changement}\:\sqrt{\mathrm{1}+{x}}={t}\:{give}\:\mathrm{1}+{x}\:={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}\:={t}^{\mathrm{2}}…