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Category: Integration

5e-4t-10e-2t-2-e-2t-2-dt-

Question Number 129038 by bramlexs22 last updated on 12/Jan/21 $$\int\:\frac{\mathrm{5e}^{\mathrm{4t}} +\mathrm{10e}^{\mathrm{2t}} +\mathrm{2}}{\mathrm{e}^{\mathrm{2t}} +\mathrm{2}}\:\mathrm{dt}\: \\ $$ Answered by liberty last updated on 12/Jan/21 $$\:\int\:\frac{\left(\mathrm{5e}^{\mathrm{2t}} +\mathrm{1}\right)\left(\mathrm{e}^{\mathrm{2t}} +\mathrm{2}\right)−\mathrm{e}^{\mathrm{2t}}…

prove-using-the-first-principle-that-the-derivative-of-sin-x-is-cox-x-and-that-the-derivative-of-cos-x-is-sinx-

Question Number 129033 by oustmuchiya@gmail.com last updated on 12/Jan/21 $${prove}\:{using}\:{the}\:{first}\:{principle}\:{that} \\ $$$${the}\:{derivative}\:{of}\:\boldsymbol{{sin}}\:\boldsymbol{{x}}\:{is}\:\boldsymbol{{cox}}\:\boldsymbol{{x}}\:{and} \\ $$$${that}\:{the}\:{derivative}\:{of}\:\boldsymbol{{cos}}\:\boldsymbol{{x}}\:{is} \\ $$$$−\boldsymbol{{sinx}} \\ $$ Commented by bramlexs22 last updated on 12/Jan/21…

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…