1. ## Calculus Integrals

I have a final exam in an hour, I get understand everything but integrals. I don't have a bloody clue.

A sample question is;

Find the following integral;

$S (x^3 + 5x - 8)/(9x^5) d/dx$

I'm just completely lost. I must have missed the class(es) when we went over this, nothing in my notes, and I can't find anything in my textbook.

I know an hour is a little short to learn this, but if someone could go over the general idea for me, I'm hoping I can steal a mark or two on those questions.

2. What in the world is the "S"? I'm assuming you're trying to do an integral sign?

So you want to find the integral of (x^3 + 5*x - 8)/(9*x^5)dx

Do you agree we can expand the above to:

1/(9*x^2) + 5/(9*x^4) - 8/(9*x^5)

Then:

Take the integral of each of the terms.

Thus,

-1/(9*x) + [-5/(27*x^3)] + [2/(9*x^4)] + C, where C is some constant.

3. Yeah, its supposed to be that extended S integral sign thingy.

But I think I'm screwed.

I sorta get how you expanded it, but I don't know where the variable X went. And I don't even know what taking the integral means.

Oh well, hopefully I'll do well in the other sections to make up for it.

4. Originally Posted by Sucker Punch
And I don't even know what taking the integral means.
It means finding the "anti-derivative".
That is a function whose derivative is equal to the function.

For example,
$\int 2x dx=x^2$
Because,
$(x^2)'=2x$

In fact,
$\int 2xdx = x^2+1$
Because the constant term vanishes when you take the derivative.

Thus, all anti-derivates must be,
$\int 2xdx=x^2+C$
Where $C$ is any konstant function.