There is much more to life than engineering.

Sorry, I should have quoted properly in my reply. My first sentence ("Yes.") was in general agreement with you, the second sentence was specifically about

> Mathematica has been able to do many integrals for decades and yet we still make students learn all the tricks to integrate by hand

But maybe, integrating by hand is still as big as ever in other parts of academia. Or were you thinking about high school? I'm fairly sure, that symbolic solving of integrals is treated as less important in education these days, than it was before digital computers, but I could be wrong. Mathematica's symbolic solve sure is very useful, but numeric solutions are what really makes the art of finding integrals much less relevant.