# Integral I can't Understand

1. Jul 31, 2015

### scottshannon

1. The problem statement, all variables and given/known data
I have posted what appears to be the solution of this integral. I don't understand how the first integral was split apart in the 3rd line.

2. Relevant equations
The solution is included

3. The attempt at a solution
I have tried to break the integral apart but cant see how to do it...

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2. Jul 31, 2015

### Dr. Courtney

Looks like it might be integration by parts.

3. Jul 31, 2015

### scottshannon

what would be the assignment of u and dv? Does the way that he solved this problem make sense to you?

4. Jul 31, 2015

### fireflies

Did you understand the second line? The third line is Int(uv)dx= u*int(v)dx- int{u'*(int v dx)}dx

Here int=integration. latex is not working here

5. Jul 31, 2015

### fireflies

It's a common formula, you must have learnt it. If you don't you will find it in your textbook. It's a necessary formula to do integration

6. Jul 31, 2015

### DeldotB

Good day. As Dr Courtney said it is in fact by parts. Once the integral is split into two let:

$$u=x$$
$$du=dx$$

$$v=-2(x^{4}+1)^{-1/2}$$
$$dv=(4x^{3})/(x^{4}+1)^{3/2}$$

On the first integral.

Good grief it's nearly impossible to type out latex on an iPad!!

7. Jul 31, 2015

### Qwertywerty

Here try this - take x2 out from the denominator , and then multiply - divide by two .

See what happens .

8. Jul 31, 2015

### scottshannon

DeldotB..Thank you... I understood that it was probably integration by parts but it wasn't immediately obvious how to make the u and dv assignment.

Qwertywerty..thank you. I took out an x^2 from the denominator and multiplied by 2 on top and bottom and then was able to let u = x^2 +x^(-2) but I would not have been able to have the presence of mind to have taken out the x^2 because I couldn't have foreseen what was going to happen...but thank you.

I cannot use Latex and would like to learn....is there a way to learn to use latex?

9. Jul 31, 2015

### Qwertywerty

What you need is practice .

10. Jul 31, 2015

### scottshannon

I have been trying to find problems of a nature that will allow me to do that...

11. Jul 31, 2015

### Qwertywerty

12. Jul 31, 2015

### scottshannon

I don't have a teacher or mentor here....I dont know anyone here.....

13. Jul 31, 2015

### Qwertywerty

I meant a teacher at your school . You can always post at the academic guidance area if you don't want to ask your teacher .

14. Jul 31, 2015

### scottshannon

Thank you but I don't go to school...I am out of school....I am just trying to learn on my own....

15. Jul 31, 2015

### Qwertywerty

My bad . I'm not sure how that works .

16. Aug 1, 2015

### scottshannon

Qwertywerty....what was it that led you to take out an from the bottom

17. Aug 1, 2015

### scottshannon

Qwertywerty....what was it that led you to take out an x2 from the bottom

18. Aug 1, 2015

### Ray Vickson

What resources are you attempting to use? I recommend highly that you buy a copy of "Schaum's Outline of Calculus" (Google 'shaums outline series'). It starts at the elementary level and takes you through all the types of things you are asking about here; it has more than 1000 solved problems where you are taken step-by-step through the solution, and it is accompanied by instructional on-line videos. It is not expensive, ranging from about $6 to$14 (used) on Amazon.

My apologies if you are using this already and it is still not enough.

19. Aug 1, 2015

### Qwertywerty

Well , I could see that taking x2 from the denominator would give you the derivative of the denominator - Practice

I'm sorry if I've said something obvious .

Last edited: Aug 1, 2015
20. Aug 2, 2015