Integration by parts

I have done the 1st part of question and the answer I got is $\frac{5e^4 - 1}{32}$which I verified from the calculator too. But I am confused how to approach to the deducing part using previous result(since it is stated HENCE ). Any help is greatly appreciated.

Answer

Substitute $t=x^2$ and you will get:

$$A = \frac 12 \int_1^e t^3(\ln\sqrt{t})^2 dt = \frac 18 \int_1^e t^3(\ln t)^2dt$$