I'm trying to integrate $\int_{-a}^a\int_b^cy^{2m+1}e^{xy^{2n}}dxdy$.But I have never seen an integral with so many parts to it and I am little overwhelmed. How do I solve this?
2026-03-25 15:57:00.1774454220
Problems with double integration
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$$\newcommand{\i}[2]{\int_{#1}{#2}}$$ I believe you can split it up like $$\int_{-a}^{a}\Biggr(\int_{b}^{c} \cdots dx \Biggr)dy$$
To learn more about double integrals, click on,
https://www.khanacademy.org/math/multivariable-calculus/integrating-multivariable-functions/double-integrals-topic/v/double-integral-1
$$\i{-a}{a} y^{2m+1-2n}(\i{b}{c} y^{2n} e^{y^{2n}x}dx)dy$$ $$\i{-a}{a} y^{2m+1-2n} e^{y^{2n}x} dy$$ Putting $e^{y^{2n}x}=t$ $$dt =y^{2n-1} e^{y^{2n}x}dx$$ $$\i{-a}{a} \frac{y^{2m+1-2n-2n+1}}{x} y^{2n-1}x e^{y^{2n}x} dy$$ For further steps go to, https://www.integral-calculator.com/#expr=y%5E%7B2%28m-n%29%2B1%7D%20e%5E%7Bxy%5E%282n%29%7D&intvar=y See the steps there