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Category: Integration

1-2-1-4-x-x-1-1-1-x-2-1-x-1-2-dx-

Question Number 129014 by bramlexs22 last updated on 12/Jan/21 $$\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\:−\frac{\mathrm{1}}{\mathrm{4}}} {x}\left({x}+\mathrm{1}\right)\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }}\:{dx}\:=?\: \\ $$ Commented by Ajao yinka last updated on 12/Jan/21 37/192…

Given-f-x-1-1-f-x-1-f-x-f-2-2-and-2-2018-x-f-2018-dx-2-a-3-b-5-c-7-d-11-e-101-f-then-a-b-c-d-e-f-

Question Number 129009 by bramlexs22 last updated on 12/Jan/21 $$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)=\frac{\mathrm{1}+\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{1}−\mathrm{f}\left(\mathrm{x}\right)}\:;\:\mathrm{f}\left(\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{and}\:\int_{\mathrm{2}} ^{\:\mathrm{2018}} \mathrm{x}.\mathrm{f}\left(\mathrm{2018}\right)\mathrm{dx}=\mathrm{2}^{\mathrm{a}} .\mathrm{3}^{\mathrm{b}} .\mathrm{5}^{\mathrm{c}} .\mathrm{7}^{\mathrm{d}} .\mathrm{11}^{\mathrm{e}} .\mathrm{101}^{\mathrm{f}} \\ $$$$\mathrm{then}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}\:+\mathrm{f}=\_\_ \\ $$ Answered by…

nice-calculus-Evaluate-I-0-1-ln-1-x-x-dx-1-x-2-

Question Number 128977 by mnjuly1970 last updated on 11/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\mathscr{E}{valuate}\:::: \\ $$$$\:\:\:\:\:\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\frac{\mathrm{1}}{{x}}\:−\:{x}\right)\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} }\:=? \\ $$$$\:\:\:\:\:\:\:\ast………………………………\ast \\ $$ Answered by abderrahimelmerrouni last…