Solved integral of the form ∫xln(αx^2+β)dx

Solved integral of the form ∫xln(αx^2+β)dx

Solution of an indefinite integral of the form ∫xln(αx^2+β)dx by the method of integration by parts, where α takes the values 1,2,3,4,5,…n; β takes the values ±1,±2,±3,±4,±5,…±m..
An example of solving integrals for α=1, β=2 is considered; α=3, β=−2; α=2, β=−4 α=4, β=1.

∫xln(αx^2+β)dx, ∫xln(x^2+2)dx, ∫xln(3x^2−2)dx, ∫xln(2x^2−4)dx, ∫xln(4x^2 +1)dx

The solution is in PDF format