Menu Close

Category: Integration

1-2sin-2-x-4cos-2-x-dx-

Question Number 27611 by NECx last updated on 10/Jan/18 $$\int\frac{\mathrm{1}}{\mathrm{2sin}\:^{\mathrm{2}} {x}\:+\:\mathrm{4cos}\:^{\mathrm{2}} {x}}{dx} \\ $$ Answered by ajfour last updated on 11/Jan/18 $$=\int\frac{\mathrm{sec}\:^{\mathrm{2}} {xdx}}{\mathrm{2tan}\:^{\mathrm{2}} {x}+\mathrm{4}}=\int\frac{{dt}}{\mathrm{2}{t}^{\mathrm{2}} +\mathrm{4}}\:\:;\left({t}=\mathrm{tan}\:{x}\right)…

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…