#### ChaoticLlama

##### Junior Member

- Joined
- Dec 11, 2004

- Messages
- 199

for the question

∫x²dx / √(x² - 1)

I made the triangle

Code:

```
/|
/ |
x / | 1
/ |
/ |
/ |
/θ_____|
√(x² - 1)
```

∫sec³(θ)

with the anti-derivative being

(1/2) [sec θ tan θ + ln|sec θ + tan θ|] + C

And when I back-substitute I first determine from the triangle that

secθ = x / √(x² - 1)

tanθ = 1 / √(x² - 1)

which gives me from the anti-derivative

(1/2) [ x / (x² - 1) + ln|(x + 1) / √(x² - 1)|]

where the answer is supposed to be

(1/2) [ x * √(x² - 1) + ln|x + √(x² - 1)|]

what am I doing wrong? please give a detailed response.