Solution of an indefinite integral of the form ∫(x^2+α)cosβxdx 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=−4, β=1, α=3, β=2 is considered; α=−2, β=3; α=5, β=4

∫(x^2+α)cosβxdx, ∫(x^2−4)cosxdx, ∫(x^2+3)cos2xdx, ∫(x^2−2)cos3xdx, ∫(x^2+5)cos4xdx

The solution is in PDF format