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Solved integral of the form ∫√xlnαxdx

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Solved integral of the form ∫√xlnαxdx

Solving an indefinite integral of the form ∫√xlnαxdx by integration by parts, where α takes the values 1,2,3,4,5...n
An example of solving integrals for α=1,2,3
∫√xlnαxdx, ∫√xlnxdx, ∫√xln2xdx, ∫√xln4xdx

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