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Author: Tinku Tara

find-dx-sin-3-x-cos-5-x-dx-

Question Number 211344 by Nadirhashim last updated on 06/Sep/24 $$\:\:\:{find}\:\int\frac{\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{3}} \left(\boldsymbol{{x}}\right)\:\boldsymbol{{cos}}^{\mathrm{5}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\: \\ $$ Answered by Frix last updated on 06/Sep/24 $$\int\frac{{dx}}{\mathrm{cos}^{\mathrm{5}} \:{x}\:\mathrm{sin}^{\mathrm{3}} \:{x}}=\int\frac{\left(\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{x}\right)^{\mathrm{4}}…

Question-211330

Question Number 211330 by RojaTaniya last updated on 06/Sep/24 Answered by mr W last updated on 06/Sep/24 $${say}\:{p}=\frac{{a}}{{b}},\:{q}=\frac{{b}}{{c}},\:{r}=\frac{{c}}{{a}} \\ $$$${pqr}=\mathrm{1} \\ $$$${p}+{q}+{r}=\mathrm{7} \\ $$$$\frac{\mathrm{1}}{{p}}+\frac{\mathrm{1}}{{q}}+\frac{\mathrm{1}}{{r}}=\mathrm{11}\: \\…

x-6-2-3-2-6-3-2-2-y-6-3-2-2-6-3-2-2-x-5-y-5-

Question Number 211331 by efronzo1 last updated on 06/Sep/24 $$\:\:\:\:\:\mathrm{x}=\frac{\sqrt{\mathrm{6}}+\mathrm{2}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}+\sqrt{\mathrm{3}}−\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\:\mathrm{y}=\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}−\mathrm{2}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}+\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\mathrm{x}^{\mathrm{5}} −\mathrm{y}^{\mathrm{5}} \:=?\: \\ $$ Answered by A5T last updated on 06/Sep/24…