Examples

A and T factors

Compute the integral:

Solution

(1) Choose .

Set because simplifies when differentiated. (By the trick: is Algebraic, i.e. more “”, and is Trig, more “”.)

Remaining factor must be :

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(2) Compute and .

Derive :

Antiderive :

Obtain chart:

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(3) Plug into IBP formula.

Plug in all data:

Compute integral on RHS:

Note: the point of IBP is that this integral is easier than the first one!

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(4) Final answer is: