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

[Sarah00]

Homework Statement

Homework Equations

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![/B]

 

[Adgorn]

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

 

[vela]

Both answers are correct.

 

[Mark44]

Homework Statement

View attachment 195086

Homework Equations

The Attempt at a Solution

My Solution:
View attachment 195087

My Friend Solution:
View attachment 195088Are we both right?
If not, who is right? and what is the mistake in other's solution!

Thanks![/B]

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 $\frac{\sec^2(x)}{2} = \frac{\tan^2(x)}{2} + \frac 1 2$