Solved integral of the form ∫xctg^2αxdx

Solved integral of the form ∫xctg^2αxdx

Solving an indefinite integral of the form ∫xctg^2(αx)dx by integration by parts, where α takes the values 1,2,3,4...n
An example of solving integrals for α=1,2,5
∫xctg^2(αx)dx, ∫xctg^2(x)dx, ∫xctg^2(2x)dx, ∫xctg^2(5x)dx

The solution is in PDF format