Is the current state of math teaching in undergrad college courses struggling with the availability of easy cheap access to Wolfram Alpha?

The homework problem below, one of 40 assigned from one community college lecture, took my son and me each several hours to solve. (He struggled because he's new at this; I struggled because I was rusty at it.) He is enrolled in a second-quarter calculus course which he's already failed once after a lifetime of not struggling in school.

Find the arclength between 2 and 5 of the function:

$f(x)$ $=$ $x^5 \over 10$ $+$ $1 \over 6x^3$

The answer is $618639 \over 2000$, taken through the arclength integral

$\int_{a}^{b} \sqrt{1+(\frac{dy}{dx})^2} dx$

That is:

$\int_{2}^{5} \sqrt{1+\frac{(-1 + x^8)^2}{4x^8}} = {618639 \over 2000}$

His question is: Why bother with the tedious symbol manipulation given WolframAlpha as a cheap tool? The answer I'm looking for is a description for why current college maths teaching still sets problem sets like this.

I can order him to buckle down for a good result and already have; no need for those "it's good for you to struggle" answers. One analogy that justifies him is the fact that teachers no longer require students to learn how to cipher a square root. So, why would we require them to go through algebra contortions like this if the tool to do the "monkey work" exists and he can spend his time reviewing its output to make sure he set the problem up right?

I disagreed: This problem exposed me to insights about the fundamental theorem of calculus and the shortcuts possible with definite integral problems. The tedious problems teach you the shortcuts Wolfram Alpha is using between steps. You're using these kinds of problems to hone your thinking skills.

Is there anything salient I could add to that argument? Is this a controversy in maths teaching, or is my son just plain wrong and needs to drill for other reasons?