Find the indefinite integral of sin(2x)(cos^2(x)) with respect to x.

We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)).

Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x).

We can now split the integral into the sum of two simpler ones with integrands 0.5sin(2x) and 0.5sin(2x)cos(2x), the latter of which is equal to 0.25sin(4x).

These integrate nicely to -0.25cos(2x)-(1/16)cos(4x) + c where c is the constant of integration.