Answer:
Step-by-step explanation:
[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]
Recall that we can express the squared trig functions in terms of cos(2x). That is,
And so inverting these,
.
Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).
Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).
So then,
This is now integrable (phew),