Solution of an indefinite integral of the form ∫xln(αx+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=5 is considered; α=−2, β=−4; α=3, β=−2; α=4, β=3
∫xln(αx+β)dx, ∫xln(x+5)dx, ∫xln(−2x−4)dx, ∫xln(3x−2)dx, ∫xln(4x+3)dx

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