# Homework Help: U substitution

1. Feb 3, 2014

### jdawg

1. The problem statement, all variables and given/known data
∫(4x)/(x2+9) dx

2. Relevant equations

3. The attempt at a solution
Originally I tried to solve with u substitution:

u=x2+9
du=2x dx
1/2du=dx
∫2/u
=2lnu+C
=2ln(x2+9)+C

But shouldn't arctan be somewhere in the answer?

2. Feb 3, 2014

### jdawg

Oops, I made a typo.
1/2xdu=dx

3. Feb 3, 2014

### SteamKing

Staff Emeritus
What's the derivative of an arctan function?

In any event, if you differentiate your answer, you should obtain the original integrand.

4. Feb 3, 2014

### jdawg

Is it (1/1+x2)?

5. Feb 3, 2014

### Curious3141

Yes, assuming you meant $\frac{1}{1+x^2}$, because your parentheses are placed wrongly. But $\frac{x}{1+x^2}$ is a completely different expression from $\frac{1}{1+x^2}$. In this case, you have something more like the former. Hence no arctan in the integral.

6. Feb 3, 2014

### jdawg

But I don't understand why u substitution doesn't work?

7. Feb 3, 2014

### Curious3141

Who said it doesn't work? Your integral in the first post is correct.

8. Feb 3, 2014

### jdawg

Really?? When I went to a tutoring center at my university the tutor told me that I needed to use arctan? Or was she just saying that its another method of doing it?

9. Feb 3, 2014

### Staff: Mentor

No. She was saying it because she was wrong.

10. Feb 3, 2014

### jdawg

Hahaha! Thanks for your help everybody :)

11. Feb 4, 2014

### gopher_p

To be fair, it's possible that by "use arctan" the tutor meant to use a trig sub $\tan\theta=x$, which would be the same as $u=\arctan x$. This would work, though it'd most definitely be a more involved approach than the simple u-sub suggested in the thread.

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