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3x-i-2x-y-dx-




Question Number 5278 by sara last updated on 04/May/16
∫{(3x)i+(2x)y}dx=
$$\int\left\{\left(\mathrm{3}{x}\right){i}+\left(\mathrm{2}{x}\right){y}\right\}{dx}= \\ $$$$ \\ $$
Answered by FilupSmith last updated on 04/May/16
∫(3xi+2xy)dx  =3i∫xdx+2y∫xdx  =(3i+2y)∫xdx  =(3i+2y)((1/2)x^2 +c)  =(1/2)x^2 (3i+2y)+c  c=constant
$$\int\left(\mathrm{3}{xi}+\mathrm{2}{xy}\right){dx} \\ $$$$=\mathrm{3}{i}\int{xdx}+\mathrm{2}{y}\int{xdx} \\ $$$$=\left(\mathrm{3}{i}+\mathrm{2}{y}\right)\int{xdx} \\ $$$$=\left(\mathrm{3}{i}+\mathrm{2}{y}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} +{c}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} \left(\mathrm{3}{i}+\mathrm{2}{y}\right)+{c} \\ $$$${c}={constant} \\ $$

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