Axio
=o
- Joined
- Mar 20, 2014
- Messages
- 484
- Gender
- Male
- HSC
- 2015
Hi guys, can anyone help me with this integral?
![](https://latex.codecogs.com/png.latex?\bg_white I=\int \sqrt{16+x^2}dx)
I know that there would be easier ways to solve it but can anyone see where I've gone wrong?
I use a trigonometric substitution and then integration by parts. Assuming my other steps are right, I get to:
![](https://latex.codecogs.com/png.latex?\bg_white \frac{I}{8}=tan\theta sec\theta +ln|tan\theta +sec\theta| +c)
And then by substituting in:
![](https://latex.codecogs.com/png.latex?\bg_white $Substituting in$ \ x=4tan\theta)
I get:
![](https://latex.codecogs.com/png.latex?\bg_white I=\frac{x}{2}\sqrt{x^2 +16}+8ln|\sqrt{\frac{x^2}{16}+1}+\frac{x}{4}|+c)
... Which doesn't seem to be the right answer :/.
EDIT:
I think my mistake is coming from substituting it back in...
I know that there would be easier ways to solve it but can anyone see where I've gone wrong?
I use a trigonometric substitution and then integration by parts. Assuming my other steps are right, I get to:
And then by substituting in:
I get:
... Which doesn't seem to be the right answer :/.
EDIT:
I think my mistake is coming from substituting it back in...
Last edited: