Problems with double integration 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?
$$\newcommand{\i}[2]{\int_{#1}{#2}}$$
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&amp;intvar=y
See the steps there
$$\newcommand{\i}[2]{\int_{#1}{#2}}$$
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&amp;intvar=y
See the steps there