Find the indefinite integral. (Use C for the constant of integration.)

(3x^2 − 2x + 1)(x^3 − x^2 + x)^7 dx

tep-by-step explanation:

In order to find the integral:

we can do the following substitution:

Let's call

Then

which allows us to do convert the original integral into a much simpler one of easy solution:

Therefore, our integral written in terms of "x" would be:

Step-by-step explanation:

Remark

The problem with this question is that you don't exactly know what the 25% does.

I think the way to do the problem is to consider where the 42 dollars comes from.

I think the beginning part of the problem is to develop an equation which you may not be able to solve.

So the cost using the 30% reduction is 0.7c where c is the original cost. But the 25% makes the actual cost for the person = 0.7c - 25% of 0.7c

The result is 42 dollars.

0.7c - 0.25*0.7c = 42

If I'm right, that can be solved.

0.7c - 0.175c = 42

0.525c = 42

c = 42/0.525

c = 80 dollars.

So before all the reductions and everything else, the case actually cost 80 dollars.