Yeah I did try searching how to integrate $e^{x^2}$ and mostly I stumbled upon how a similar but not this function called Gaussian function $e^{-x^2}$ is un-integrable , now I was given to solve a differential equation $$xe^{x^2}dx + (y^5-1)dy = 0$$ so how do I proceed with the part of integrating $xe^{x^2}dx$ ? I have tried a lot, any help will be appreciated.
2026-04-07 10:24:44.1775557484
How do we integrate $xe^{x^2}$ in this differential equation?
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To find $$\int xe^{x^2}dx$$ Set $t=x^2$, $$\frac12\int e^tdt=\frac12e^{x^2}+C$$ Beware, changing the integrand from $xe^{x^2} $ to $e^{x^2}$ makes a hell lot of a difference. Here, you have a $f(g(x))g'(x)$ form, but you changed it to $f(g(x))$ form.