When the World is Ending, Use Integration by Parts

The most useful technique in all of integration, this is integration by parts.
The title is a joke that is passed around in the maths community, which simply highlights how powerful this method of integration is. We look at how we derive the famous equation, which is simply by arranging the terms in the product rule equation in a specific way, and once we have it in our preferred format we see how powerful this method really is. We learn how to choose u and dv/dx as well, using the acronym LIATE, which stands for Logarithms, Inverse, Algebraic, Trigonometric and Exponential. We go through a worked example as well.
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Question taken from: CIE 9709 Summer 2023 Paper 31
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