Solving a double interated integral

Question

$$\int_{-a}^{a}\int_b^cy^{2m+1}e^{xy^{2n}}dxdy$$, where $a>0$ and $b>c$ are real numbers and $n$ and $m$ natural numbers such that $2(m-n)>1$.

So far, I have been able to use substitution $u=xy^{2n}$ to solve the middle integral and get $$ \int_{-a}^{a}y^{2m+1-2n}(e^{cy^{2n}}-e^{by^{2n}})dy$$

What should I do next?

Answer 1

Hint

You properly arrived to the difference of two integrals which look like $$\int_{a}^{-a}y^{2m-2n+1}\,e^{\alpha y^{2n}}\,dy$$ and the integrand is odd and the bounds are symmetrical.

Then .... ???