# Integration. Where is the mistake? (if there is)

1. Apr 16, 2017

### Sarah00

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
My Solution:

My Friend Solution:

Are we both right?
If not, who is right? and what is the mistake in other's solution!

Thanks!!

2. Apr 16, 2017

You are correct. The problem with your friend's solution is the integration itself, what is the integral of tan(x)sec2(x)?

3. Apr 16, 2017

### vela

Staff Emeritus
Both answers are correct.

4. Apr 16, 2017

### Staff: Mentor

Your solution is correct, and your friend's solution is almost correct. Your friend wrote $\frac{\tan x^2} 2 + C$, but possibly meant to write $\frac{\tan^2(x)} 2 + C$. Although this is different from what you found, the corrected answer from your friend differs only by a constant from your answer. Note that $\sec^2(x) = \tan^2(x) + 1$, so $\frac{\sec^2(x)}{2} = \frac{\tan^2(x)}{2} + \frac 1 2$