The task is to find volume of a solid given by this system of inequalities: $$ \left\{ \begin{array}{c} \left(\frac{x}{4}\right)^8 + \left(\frac{|y|}{5}\right)^5 < 1 ,\\ \left(\frac{x}{4}\right)^8 + \left(\frac{|z|}{3}\right)^{40/27} < 1 . \end{array} \right. $$ I tried this: $$V = \iiint \,dx\,dy\,dz$$ $$ 4u = x, 5v = y, 3w = z$$ So, $$ \begin{split} V &= 60\iiint \,du\,dv\,dw \\ &= 60 \int_{-1}^{1}du \int_{-(1-u^8)^{1/5}}^{(1-u^8)^{1/5}} dv \int_{-(1-u^8)^{27/40}}^{(1-u^8)^{27/40}} dw \\ &= 240 \int_{-1}^{1}(1-u^8)^{7/8}du \end{split} $$
And I got stuck here. Is my solution right and, if so, how can I solve the last integral? And if this solution is wrong, how can I solve this problem in other way?