Calculate the integral from 0 to pi/2 of sin^2(x) dx.

Find the integral of sin(5x)cos(2x) dx.

Find \( \int 5\cos^2(4x) \, dx \).

Calculate \( \int_0^{\pi} \sin^2(x) \, dx \).

Calculate the integral of sin^2(x) dx.

Calculate the integral of cos^2(2x) dx.

Calculate the integral of sin^3(2x) dx.

Calculate the integral from 0 to π/2 of cos^2(2x) dx.

Calculate the integral from 0 to π of 2sin^2(5x) dx.

Calculate the integral from 0 to π/4 of cos^3(3x) dx.