# Integration problem

1. May 20, 2010

### mk200789

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

integrate (x^3)sqrt(x^2 + 8) dx

2. Relevant equations

3. The attempt at a solution

let x = 2sqrt(2)tan(t) ==> dx= 2sqrt(2)sec^2(t) dt

=int (x^3)sqrt(x^2 + 8) dx
=int (16sqrt(2)tan^3(t)) sqrt(8tan^2(t) + 8) (2sqrt(2)sec^2(t)) dt
=int (32 sqrt(2)) (tan^3(t)) sec^3(t) dt

my problem is till this point i compared it with the the prof. working

help~

2. May 21, 2010

### vela

Staff Emeritus
Your work is fine. It looks like your professor didn't substitute for dt.

3. May 21, 2010

### julian92

I didn't really take a look at your solution

But in order to solve the integral ,, just substitute >>> u = 8 + x^2

it's straight forward ;)

4. May 21, 2010

### Cyosis

It may be straightforward but this substitution is pretty useless.

Integration by parts is the way to go here and you only have to do it once.

5. May 21, 2010

### Gib Z

The solution comes out almost straight away with the substitution actually.

6. May 21, 2010

### Cyosis

While useless may have been a bit strong I still feel you don't gain much by doing that substitution. You will have to do integration by parts after wards, which you may as well do right away.

7. May 21, 2010

### Char. Limit

How exactly? du does not equal x^3, it equals 2x. Rather useless.

8. May 21, 2010

### Cyosis

The idea is that x^2=u-8 and we can write x^3 as x^2*x. You can then combine them. However in my eyes that just sends you back to the original problem. We may be going a bit off topic here.

9. May 21, 2010

### mk200789

SO.........my working so far is correct? or the prof's correct?:|

10. May 21, 2010

### Dickfore

try the substitution

$$t = \sqrt{x^{2} + 8}$$

11. May 21, 2010

### Cyosis

You are correct. However unless the exercise asks you to specifically use a trigonometric substitution you should really use integration by parts.

12. May 21, 2010

### mk200789

thanks. yeh i was told to use trig sub:)

13. May 21, 2010

### Cyosis

I just noticed that you made a minor mistake regarding the constant factors.

This is correct.

Here you made a mistake when it comes to multiplying the constant roots.

14. May 21, 2010

### vela

Staff Emeritus
No integration by parts is needed with the substitution. You just multiply it out to get two terms of the form u^n.