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Category: Integration

0-ln-x-2-x-x-1-x-dx-

Question Number 151519 by talminator2856791 last updated on 21/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{ln}\left(\lfloor{x}^{\mathrm{2}} \rfloor!\right)}{\:\left({x}^{{x}} +\mathrm{1}\right)^{{x}} }\:{dx} \\ $$$$\: \\ $$ Terms of Service Privacy…

log-x-1-x-x-dx-

Question Number 151501 by talminator2856791 last updated on 21/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\left(\mathrm{log}\:{x}\:+\:\mathrm{1}\right){x}^{{x}} \:{dx} \\ $$$$\: \\ $$ Answered by puissant last updated on 21/Aug/21 $${K}=\int\left(\mathrm{1}+{lnx}\right){x}^{{x}}…

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

Question Number 85952 by jagoll last updated on 26/Mar/20 $$\int\:\:\frac{\sqrt{\mathrm{x}}}{\mathrm{2}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}}}\:\mathrm{dx}\: \\ $$ Answered by john santu last updated on 26/Mar/20 $${let}\:{t}^{\mathrm{6}} \:=\:{x}\:\Rightarrow{dx}\:=\:\mathrm{6}{t}^{\mathrm{5}} \:{dt} \\ $$$$\int\:\:\frac{{t}^{\mathrm{3}}…

xdx-x-4-4x-2-5-

Question Number 151461 by peter frank last updated on 21/Aug/21 $$\int\frac{\mathrm{xdx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{2}} +\mathrm{5}} \\ $$ Answered by puissant last updated on 30/Aug/21 $${I}=\int\frac{{x}}{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} +\mathrm{5}}{dx}=\int\frac{{x}}{\left({x}^{\mathrm{2}}…