# Integral help

1. Feb 1, 2008

### nuclearrape66

how do i integrate 1/(x^2 +4)?

2. Feb 1, 2008

### Feldoh

What's the derivative of arctan?

3. Feb 1, 2008

1/1+x^2

4. Feb 1, 2008

### Feldoh

See how that might be helpful?

5. Feb 1, 2008

### rock.freak667

$$\int \frac{1}{x^2 +4} dx$$

$$= \int \frac{1}{x^2 +(2)^2} dx$$

try x=2tan$\theta$

6. Feb 1, 2008

### nuclearrape66

hmm lemem see...1 second

7. Feb 1, 2008

### rohanprabhu

Exactly.. so now from your function, you take 4 common, you get:

$$\frac{1}{4}\int\frac{1}{({\frac{x}{2}})^2 + 1}dx$$

Now, if you take $\frac{x}{2} = y$.. you can solve this integral.. get a hint?

Once you have done this, it would be helpful for you to remember the formula for a general case as in $$\int\frac{1}{a^2 + x^2}dx$$

8. Feb 1, 2008

### Feldoh

Yeah rohan's post is what I was think too..

9. Feb 1, 2008

### nuclearrape66

oh i see, thanks

and quick response from everyone =)

10. Feb 2, 2008

### fermio

$$\int\frac{1}{x^2+a^2}dx=\frac{1}{a}\arctan\frac{x}{a}+C$$
$$\int\frac{1}{x^2+2^2}dx=\frac{1}{2}\arctan\frac{x}{2}+C$$

11. Feb 2, 2008

### Feldoh

No need to post the solution he all ready figured it out...