For some reason I am having trouble with the integral: sin^{2}xcos^{2}x dx

I have tried a few identities with no luck.

1st try

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(1/2) | (2sinxcosx)^{2}dx

2nd try

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(1/4) | (1 - cos(2x))(1 + cos(2x)) dx

The website I am looking at keeps saying to use integration by parts, which makes no sense to me.

Thanks for your help.