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Category: Integration

Question-87585

Question Number 87585 by Power last updated on 05/Apr/20 Answered by redmiiuser last updated on 05/Apr/20 $${arc}\mathrm{sin}\:{x}+\mathrm{arccos}\:{x}=\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{arcsin}\:{x}.\mathrm{arccos}\:{x}=\frac{\pi}{\mathrm{2}}\mathrm{arcsin}\:{x}−\left(\mathrm{arcsin}\:{x}\right)^{\mathrm{2}} \\ $$$$\mathrm{arcsin}\:{x}={t} \\ $$$${dx}=\mathrm{cos}\:{t}.{dt} \\ $$$${x}=\mathrm{sin}\:{t}…

0-1-log-1-x-1-x-2-dx-

Question Number 153114 by peter frank last updated on 04/Sep/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{log}\:\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by puissant last updated on 04/Sep/21 $${x}={tan}\left({u}\right)\:\rightarrow\:{dx}=\mathrm{1}+{tan}^{\mathrm{2}} {udu}…