Is This Integral Calculation Correct?

[lemon26]

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

Homework Statement

Integrate (5x^2 + √x - 4/x^2) dx

Homework Equations

I think this is differentiating by parts...

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!

 

[phyzguy]

Two questions for you:

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

 

[SteamKing]

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

 

[Ray Vickson]

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

Homework Statement

Integrate (5x^2 + √x - 4/x^2) dx

Homework Equations

I think this is differentiating by parts...

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!

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
$$(4) \;\int \left(5 x^2 - \sqrt{ \frac{x-4}{x^2} } \right)\, dx$$