If you have [tex] \int e^{x^{2}}x^{2} [/tex] would it be reasonable to choose [tex] u = e^{x^{2}}, dv = x^{2}, du = 2xe^{x^{2}}, v = \frac{x^{3}}{3} [/tex]? And then I get [tex] x^{3}e^{x^{2}} - 2\int x^{4}e^{x^{2}} [/tex]. Would this be equivalent to choosing [tex] u = x, dv = 2xe^{x^{2}}, v = e^{x^{2}}, du = dx [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

This was for solving a differential equation:

[tex] \frac{dy}{dx} + 2xy = x^{2} [/tex], where [tex] P(x) = 2x, Q(x) = x^{2}, I = e^{\int 2x} = e^{x^{2}} [/tex]. So [tex] (ye^{x^{2}})' = e^{x^{2}}x^{2} [/tex]

[tex] y = e^{-x^{2}} \int e^{x^{2}}x^{2} dx + C [/tex]

Thanks

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# Homework Help: Integration by Parts/Differential Equation

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