
Taking

gives

, so that the integral becomes





When

, we have


and from here we can substitute

to proceed from here.
Quick note: When we set

, we are implicitly enforcing

just so that the substitution can be undone later via

. But note that over this domain, we automatically guarantee that

, so the absolute value bars can be dropped immediately.
1. D
2. B
3. A
Hope this help :)
Option C:
The coefficient of
is 40.
Solution:
Given expression:

Using binomial theorem:

Here 
Substitute in the binomial formula, we get

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.


Let us solve the term one by one.






Substitute these into the above expansion.

The coefficient of
is 40.
Option C is the correct answer.