Year 1 Sem 2/LC Mathematics for Physicists 1B/Lecture 20
The derivative of an elementary function is always an elementary function. The integral of an elementary function is not always elementary however.
As a result, differentiation is always purely algorithmic churn, integration is often tricky.
Methods of integration are often based on methods of differnetiation, for example:
- Integration by inspection: just spotting the answer.
- Integration by parts: Inverse of the product rule of differentiation.
- Integration by substitution: Inverse of the chain rule of differentiation.
Integration By Inspection
This is the most difficult to codify and can be easy for some people and very easy for others.
This might involve:
- Trigonometric Identities, for example replacing an expression whose integral is unknown with an expression whose integral is, using a trig sub.