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∫cos^5 x sin^5 x dx

I thought I would try to solve this by first doing:

∫(1 - sin^2 x) cos^3 x sin^5 x dx

but would like to know if that's right.

[Edit] Is the answer something like (sin^6 x) / 6 - (sin^8 x) / 4 + (sin^10 x) / 10 ?[Edit]

I thought I would try to solve this by first doing:

∫(1 - sin^2 x) cos^3 x sin^5 x dx

but would like to know if that's right.

[Edit] Is the answer something like (sin^6 x) / 6 - (sin^8 x) / 4 + (sin^10 x) / 10 ?[Edit]

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