Can't really wrap my head around this integral. I tried doing some u-subs, but it just doesn't get much easier. Would really appreciate any help.
$$\int_{0}^{\pi} \frac{x(\sin x)^6}{(\sin x)^6+ (\cos x)^6}\,\mathrm dx$$
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Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Jul 09 '23 at 09:58
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Even though the duplicate uses the exponent $2018$, the accepted answer works with any even exponent, including the $6$ present here. – Sarvesh Ravichandran Iyer Jul 09 '23 at 11:32
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Thanks a lot for the help! – David Dragan Jul 09 '23 at 17:09