Solved integral of the form ∫ln(sinαx)/cos^2(αx)dx

Solved integral of the form ∫ln(sinαx)/cos^2(αx)dx

Solution of an indefinite integral of the form ∫ln(sinαx)/cos^(αx)dx by the method of integration by parts, where α takes the values 1,2,3,4,5,…n.
An example of solving integrals for α=1, α=2, α=5 is considered.

∫ln(sinαx)/cos^2(αx)dx, ∫ln(sinx)/cos^2(x)dx, ∫ln(sin2x)/cos^2(2x)dx, ∫ln(sin5x)/cos^ 2(5x)dx

The solution is in PDF format