1.

Do the anti-derivative on the integrand.

Final Answer

and this problem

2.

Next taking the derivative of the highest power in the integrand (BUT WAIT - 3 is not the derivative)

Next flipping the so it becomes

The stuff to the right of the left linear factor (integrand) disappears. Now we do the anti-derivative on the integrand.

Final Answer

As you can see that in the 2nd problem the is a flipped version of 3 which came from the in the beginning (since that was the largest power).

But in the 1st problem the highest power is not made into 3 and flipped.

But I see a problem in the reasoning: differentiated is [tex]3x^{2}[tex] not 3. So why does the 3 come about? Where did it come from?