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Category: Integration

BeMath-1-cos-ln-x-dx-2-sin-ln-x-dx-

Question Number 108597 by bemath last updated on 18/Aug/20 $$\:\:\:\:\:\frac{\angle\:\mathcal{B}{e}\mathcal{M}{ath}\angle}{\nparallel} \\ $$$$\left(\mathrm{1}\right)\:\int\:\mathrm{cos}\:\left(\mathrm{ln}\:{x}\right)\:{dx}\: \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{sin}\:\left(\mathrm{ln}\:{x}\right)\:{dx}\: \\ $$ Answered by 1549442205PVT last updated on 18/Aug/20 $$\mathrm{Set}\:\mathrm{I}=\int\mathrm{cos}\left(\mathrm{lnx}\right)\mathrm{dx},\mathrm{J}=\int\mathrm{sin}\left(\mathrm{lnx}\right)\mathrm{dx} \\…

Question-108593

Question Number 108593 by Rasikh last updated on 18/Aug/20 Answered by Her_Majesty last updated on 18/Aug/20 $$\left(−\mathrm{1}\right)^{{x}} ={e}^{{xln}\left(−\mathrm{1}\right)} ={e}^{{i}\pi{x}} ={cos}\pi{x}+{isin}\pi{x} \\ $$$$\Rightarrow\:\int\left(−\mathrm{1}\right)^{{x}} {dx}=\frac{\mathrm{1}}{\pi}\left({sin}\pi{x}−{icos}\pi{x}\right)+{C} \\ $$…

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

Question Number 108582 by mathmax by abdo last updated on 17/Aug/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 18/Aug/20 $$\mathrm{x}=\mathrm{tan}\left(\mathrm{t}\right)\Rightarrow\:\Omega=\int_{\mathrm{0}}…