Integral of trig functions

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[hollow coyote]

I have to do the previous problem, I have the following procedure:

where did I make a mistake? I really don't know

[noble folio]

notice that
4sin⁴(x)cos²(x) = sin²(2x)sin²(x)

[hollow coyote]

I see

[crude heart]

It looks from a cursory glance that your u-substitution might be wrong

What is t again? What is dt?

dt won’t be 1

[hollow coyote]

oh yes

it'd be 2