# Homework Help: Basic Integral

1. Oct 25, 2006

### danago

Hey. Say i was given this indefinite integral to evaluate:

http://img126.imageshack.us/img126/6374/aaaaog3.gif [Broken]

How could i do that? I can do it by first expanding it all, but that takes a very long time and is quite tedious, especially with such a large index as 7. Is there another way i can do that?

Thanks,
Dan.

Last edited by a moderator: May 2, 2017
2. Oct 25, 2006

### StatusX

You could use substitution.

3. Oct 25, 2006

### danago

What would i substitute out? I tried using substitution, but couldnt get very far.

4. Oct 25, 2006

### danago

http://img109.imageshack.us/img109/8527/aaaaac7.gif [Broken]

Where from there?

Last edited by a moderator: May 2, 2017
5. Oct 25, 2006

### HallsofIvy

Why squared? that leaves a fraction power. I would just let
u= 3x+2 then du= 3dx so dx= (1/3)du. Also, x= u/3+ 2/3 so
x(3x+2)7dx= (u/3+ 2/3)(u7)(1/3du)= (1/9)(u8+ 2u7)dx

Danago, you have remember to replace dx with du. If u= (3x+2)2, then du= 2(3x+2)dx= (6x+ 4)dx. I think courtrigrad's point was that you can use that "x" in the integeral to help with that. But with that "4dx" still left, I think u= 3x+2 is simpler.

6. Oct 25, 2006

doesn't x = u/3 - 2/3

7. Oct 25, 2006

### danago

Hmmm...im a bit lost. I understand up to "dx= (1/3)du", but where does the "x= u/3+ 2/3" come from? If it is anything more advanced than substitution, i think ill leave it there, because i just made this question up out of curiosity, not because i need to know it for school, and even substitution is more advanced than what we've been doing at school, but i learnt it to make some of the question we do simpler.

8. Oct 25, 2006

If u = 3x +2, then x = u/3 - 2/3. You have to solve for x.

9. Oct 25, 2006

### danago

oh lol. That simple :P

10. Oct 25, 2006

### danago

Is this right?
http://img150.imageshack.us/img150/1972/aaaaka4.gif [Broken]

Last edited by a moderator: May 2, 2017
11. Oct 25, 2006

### Max Eilerson

Yes it's correct, but you can tidy it up a little.

12. Oct 25, 2006

### danago

ok thanks everyone :)