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Category: Integration

help-dx-csc-x-1-my-way-dx-1-sinx-1-sinx-1-sinx-dx-sinx-1-1-sinx-1-dx-1-1-sinx-1-dx-1dx-sinx-1-sinx-1-sinx-1-dx-x-C-si

Question Number 33009 by kyle_TW last updated on 09/Apr/18 $${help}\:!\:!\:! \\ $$$$\int\:\frac{{dx}}{{csc}\left({x}\right)−\mathrm{1}}\:=\:? \\ $$$$ \\ $$$$\left[\:{my}\:{way}\:\right] \\ $$$$\int\left(\:\frac{{dx}}{\frac{\mathrm{1}}{{sinx}}\:−\:\mathrm{1}}\:\right) \\ $$$$=\int\frac{{sinx}}{\mathrm{1}−{sinx}}\:{dx} \\ $$$$=−\int\:\frac{{sinx}−\mathrm{1}+\mathrm{1}}{{sinx}−\mathrm{1}}\:{dx} \\ $$$$=−\int\mathrm{1}+\frac{\mathrm{1}}{{sinx}−\mathrm{1}}\:{dx} \\…

Integrate-the-function-f-x-y-xy-x-2-y-2-over-the-domain-R-3-x-2-y-2-3-1-xy-4-

Question Number 98520 by bobhans last updated on 14/Jun/20 $$\mathrm{Integrate}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{xy}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right) \\ $$$$\mathrm{over}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{R}:\left\{−\mathrm{3}\leqslant\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \leqslant\mathrm{3},\:\mathrm{1}\leqslant\mathrm{xy}\leqslant\mathrm{4}\right\} \\ $$ Answered by john santu last updated on…

Question-32958

Question Number 32958 by artibunja last updated on 07/Apr/18 Commented by MJS last updated on 07/Apr/18 $$\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{10}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}+\frac{\left(−\mathrm{3}+\frac{\mathrm{5}}{\mathrm{3}}\right){x}+\left(−\mathrm{10}−\frac{\mathrm{2}}{\mathrm{3}}\right)}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{4}}{\mathrm{3}}×\frac{{x}+\mathrm{8}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}} \\ $$$$\mathrm{3}{x}^{\mathrm{2}}…