What is the antiderivative of sin^2(x)cos^2(x)?

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),

step-by-step explanation: