If you hate integration like I do...

I guess everyone is busy mugging for blocks (and hence the hiatus of the blog ><). But anyway, let me share a shortcut with you guys...

The killer topic for Math block test is definitely INTEGRATION, and we know it sucks for many reason. The most tormenting part, IMO, must be integration by parts. Personally I hate writing long long expressions, moving bulks of expressions here and there, then end up in a zzz careless mistake.

Let me introduce a shortcut which is super useful and easy :) This technique is known as tabular integration by parts.

Suppose you want to solve Not an easy task, if you have tried it in your tutorials. In this technique, we still apply LIATE and let u be x^3 and v' be cos x. Now create a table and write:

Derivatives of u (Column A)	Integrals of v (Column B)

Such that column A represents the subsequent derivative of u and column B represents the subsequent integrals of v. Repeat this until you can no longer continue, for instance when u arrive at 0. Now, the answer is simply:

Which is arrived by pairing the 1st term in A with the 2nd term in B , the 2nd term in A with the 3rd term in B, the 3rd term in A with 4th term in B, etc. Take note of the ALTERNATING sign in front of each terms too.

Another example:

Derivatives of u (Column A)	Integrals of v (Column B)

Then,

Which can be solved easily to yield:

Visit http://en.wikipedia.org/wiki/Integration_by_parts#Tabular_integration_by_parts for more information. My senior used this and saved a lot of time. However, do show your full working still (I can't guarantee that your tutors will accept such cheapskate method). Use it wisely and pwn the block test :P

Cheers,

Khor Shi-Jie