1. Sep 14, 2013

### lemon26

Hi, can anyone help please as I'm getting tied up in knots...

1. The problem statement, all variables and given/known data

Integrate (5x^2 + √x - 4/x^2) dx

2. Relevant equations

I think this is differentiating by parts...

3. The attempt at a solution

So far I've got to: 5x^3 / 3 + 2x^3/2 / 3 + 4 / x +c

I can't think how I can make it any tidier so any tips would be really appreciated!

2. Sep 14, 2013

### phyzguy

Two questions for you:

(1) What is:
$$\int( f(x) + g(x)) dx$$
(2) What is:
$$\int x^k dx$$

3. Sep 14, 2013

### SteamKing

Staff Emeritus
Question (3): What is 'differentiating by parts'?

4. Sep 14, 2013

### Ray Vickson

Because you do not use parentheses, I cannot figure out whether you mean
$$(1) \; \int \left(5 x^2 + \sqrt{x} - \frac{4}{x^2} \right) \, dx \leftarrow \text{ what you wrote}$$
or
$$(2) \; \int \left( 5 x^2 + \sqrt{x - \frac{4}{x^2}} \right) \, dx$$
or
$$(3) \;\int \left(5 x^2 - \frac{ \sqrt{x-4}}{x^2} \right)\, dx$$
or
$$(4) \;\int \left(5 x^2 - \sqrt{ \frac{x-4}{x^2} } \right)\, dx$$