Examples

A and T factors

Compute the integral:

Solution

(1) Choose and :

Set because simplifies when differentiated.

(By the trick: is Algebraic, i.e. more “”, and is Trig, more “”.)

Remaining factor must be .

---

(2) Compute and :

Key chart:

---

(3) Evaluate IBP formula:

Why IBP?

The rationale of IBP is that is easier to compute than .

Hidden A

Compute the integral:

Solution

(1) Choose :

Because Log is farthest left in LIATE.

Therefore we must choose .

---

(2) Compute and :

We have and . Obtain chart:

---

(3) Evaluate IBP formula:

Perform new integration:

Final answer is: