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Category: Integration

x-2-xsin-x-cos-x-2-dx-

Question Number 37316 by rahul 19 last updated on 11/Jun/18 $$\int\:\frac{{x}^{\mathrm{2}} }{\left({x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:=\:? \\ $$ Answered by ajfour last updated on 11/Jun/18 $${let}\:{x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\mathrm{sin}\:\left({x}+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}}\right)…

calculate-dz-z-3-8-in-those-cases-1-z-C-z-1-2-z-C-z-3-

Question Number 37303 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\:\int_{\gamma} \:\:\:\:\:\:\frac{{dz}}{{z}^{\mathrm{3}} \:+\mathrm{8}}\:{in}\:{those}\:{cases} \\ $$$$\left.\mathrm{1}\right)\:\gamma\:=\left\{{z}\in{C}\:/\:\mid{z}\mid\:=\mathrm{1}\right\} \\ $$$$\left.\mathrm{2}\right)\:\gamma\:=\left\{{z}\in{C}\:/\:\mid{z}\mid\:=\mathrm{3}\right\} \\ $$ Commented by prof Abdo…