Integration by Parts is made of product rule of differentiation. The derivative of \(uv\) is \(u’v + uv’\) and integrate both sides. \( \begin{aligned} \require{color} (uv)’ &= u’v + uv’ \\ uv &= \int u’v + \int uv’ \\ \int u’v &= uv – \int uv’ \text{ or } \int uv’ = uv – \int […]

For Integration Recurrence Formula or reduction formula, it is important to set a relationship between two consecutive terms by using mostly the integration by parts. Worked Example of Integration Reduction Formula Question 1 For any integer \(m \ge 0\) let \(\displaystyle I_m = \int_{0}^{1} x^m (x^2 – 1)^5 dx \).Prove that for \( \displaystyle m\ge […]