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Category: Integration

Question-158674

Question Number 158674 by cortano last updated on 07/Nov/21 Commented by tounghoungko last updated on 07/Nov/21 $${I}_{\mathrm{1}} =\int\:\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{4}}]{{x}}}\:;\:{x}={r}^{\mathrm{12}} \\ $$$${I}_{\mathrm{1}} =\int\:\frac{\mathrm{12}{r}^{\mathrm{11}} }{{r}^{\mathrm{4}} +{r}^{\mathrm{3}} }\:{dr}=\int\:\frac{\mathrm{12}{r}^{\mathrm{8}} }{{r}+\mathrm{1}}\:{dr}…

find-D-xy-x-2-y-2-dxdy-with-D-x-y-R-2-x-2-2y-2-1-x-0-y-0-

Question Number 27595 by abdo imad last updated on 10/Jan/18 $${find}\:\:\int\int_{{D}} \:\:{xy}\sqrt{\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:{dxdy}\:\:\:{with} \\ $$$${D}=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\:\:,{x}\geqslant\mathrm{0}\:,{y}\:\geqslant\mathrm{0}\right\} \\ $$ Commented by abdo imad…

find-the-general-solution-to-1-a-sin-x-b-cos-x-dx-and-1-a-cos-x-bsin-x-dx-where-a-b-are-constants-

Question Number 93098 by Rio Michael last updated on 10/May/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to} \\ $$$$\:\int\:\frac{\mathrm{1}}{{a}\:\mathrm{sin}\:{x}\:+\:{b}\:\mathrm{cos}\:{x}}\:{dx}\:\:\mathrm{and}\:\int\:\frac{\mathrm{1}}{{a}\:\mathrm{cos}\:{x}\:−\:{b}\mathrm{sin}\:{x}}\:{dx} \\ $$$$\mathrm{where}\:{a}\:,\:{b}\:\mathrm{are}\:\mathrm{constants}. \\ $$$$ \\ $$ Commented by prakash jain last updated…

I-dx-1-x-6-

Question Number 158591 by cortano last updated on 06/Nov/21 $$\:{I}=\int\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{6}} }\:=? \\ $$ Commented by tounghoungko last updated on 06/Nov/21 $${I}=\int\:\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}−\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}…