Compute the ratio : $\frac{\int_{0}^{\pi/2}\sin^{√2+1}xdx}{\int_{0}^{\pi/2}\sin^{√2-1}xdx}$

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I want to find the ratio of the following : $$ \frac{\int_{0}^{\pi/2}\sin^{√2+1}xdx}{\int_{0}^{\pi/2}\sin^{√2-1}xdx} $$

I have tried a lot but can't solve it. Please help. Thanks.