Integral quotient by L'Hopital

Let $\phi:(-1,1)\to\mathbb{R}$ be defined by $$\phi(x)=\int_{x^{7}}^{x^{4}}\frac{1}{1+t^{3}}\,dt.$$ If $\alpha=\lim_{x\to 0}\dfrac{\phi(x)}{e^{2x^{4}}-1}$, then $42\alpha$ is equal to __________.