P4.6.2 - Integration by substitution and parts

Simple cases of integration by Students will be expected to use a substitution to find, e.g. substitution and integration by ∫ x x − 2 dx parts.; Understand these methods as the reverse processes of the chain The substitution will be given in more complicated and product rules respectively. integrals. ∫ The integral ln x dx is required.; More than one application of integration by parts may be required, for example, ∫ x2ex dx, ∫ ex sin x dx.

Use integration by substitution and parts to connect the rule to the data and decision in the question.

This matters because integration by substitution and parts determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply integration by substitution and parts to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Integration by substitution and parts is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.