Here is a formula, which is included in the textbook (Example 6, pages 248-249, sixth edition of advanced mathematics textbook of Tongji University).

Formula: ∫ [0→π] xf (sinx) dx = (π/2) ∫ [0→π] f (sinx) dx.

Note: cos in the title? X can be seen as 1-sin? Therefore, x is a function of sinx.

This is the original example. See for yourself. If you need me to write the derivation process of the formula for you, ask again.

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