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Integration by parts

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In this problem I am asked to use integration by parts utilizing the formula:
∫udv = uv - ∫vdu

Please show the values of u, dv, du, and v and each of the steps to achieve the solution. This problem may involve more than one sequence in integrating by parts. Thank you.

∫4xsec²2xdx

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This provides an example of integrating by parts.

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