# Need help with integration

1. Nov 13, 2005

### Swatch

I am trying to integrate sqrt(1+4*x^2)
I have been trying to rewrite this into sqrt(-4x+(2x + 1)^2) and putting u=2x+1 and substituting but I don't think that makes this any easier. Could someone please give me a hint.

2. Nov 13, 2005

### marlon

The answer is Partial Integration...Give it a try and let me know

marlon

edit hint : do the partial integration right a way with the sqrt(1+4x^2)dx. After this you will need to apply the (+1 -1) trick in the integrand's numerator. If you want you can first do the substitution u=2x to get rid of the 4, but it is not compulsory...

Last edited: Nov 13, 2005
3. Nov 13, 2005

### Swatch

After some hard work and a lot of eraser I got the right answer. Thank you marlon.

4. Nov 13, 2005

### amcavoy

Also:

$$\int\sqrt{1+\left(2x\right)^2}\,dx=\frac{1}{2}\int\cosh^2{x}\,dx$$

Then use the identity for the double angle to simplify that integral.

5. Nov 13, 2005

### benorin

Try $$x=\frac{1}{2}\tan \theta \Rightarrow \sqrt{1+4x^2}=\sec\theta$$.