# How to do these integrals?

1. Jan 27, 2009

### lastdayx52

a. $\int x*ln(2x) dx$
b. $\int \frac{x^2}{x^2-4} dx$

My Attempt:
a. I have abs. no clue how to start it off. Do you start it off using integration by parts?
b. Same with this. I don't know how to start it off.

"Random" Questions:
1) What does "converge" and "diverge" mean? i.e. Another question asks "Determine if each integral converges or diverges". I can do the integrals, but I'm not sure what its asking. One results in the answer being pi/3, the other results in infinity.
2) When the question tells you to setup an integral for a volume of a solid generated when the region is rotated about the line x=-2 using cylindrical shells, you just do:
$\pi * \int (f(x)+2)^2 dx$
Correct?

Thanks!

P.S. I'm not asking for answers, but rather how to start them off. Maybe 1 or 2 beginning steps in integrating these? =D

Last edited: Jan 27, 2009
2. Jan 27, 2009

### gabbagabbahey

Hi lastdayx52, welcome to PF

Let's start with a) and b).... For a) try integration by parts....For b), hint: $x^2=(x^2-4)+4$

Give it a shot and post your attempt if you require further assistance.

3. Jan 27, 2009

### lastdayx52

Got a:
$\frac{x^2*(2*ln(2)-1)}{4}+\frac{x^2*ln(x)}{2} + C$
Checked on calculator, and was correct. Thank you!

Now for b, that doesn't help me at all... >.>

4. Jan 27, 2009

### gabbagabbahey

Why not?

$$\int \frac{x^2}{x^2-4} dx=\int \frac{(x^2-4)+4}{x^2-4} dx=\int \frac{x^2-4}{x^2-4} dx +\int \frac{4}{x^2-4} dx$$

5. Jan 27, 2009

### lastdayx52

LOL haha... See I did that, but stupidly thought the integral of 1 = 1, and when checked against the calculator, it was obviously not correct. haha... Thanks! =P