Evaluate the definite integral

[crybllrd]

Homework Statement

$\int^{\frac{\pi}{4}}_{0}\frac{1+cos^{2}(x)}{cos^{2}(x)}$

Homework Equations

The Attempt at a Solution

I tried u-sub, splitting it up into 2 fractions, and a trig identity (cos^2x=(1+cos2x)/2).
Am i missing something? The other problems were quite easy.

 

[micromass]

What did you get if you split it up in two fractions? Why didn't it work?

 

[crybllrd]

I got two fractions, 1/cos^2(x) and cos^2(x)/cos^2(x)=1

I wasn't sure how to integrate the 1/cos^2(x)

 

[micromass]

I wasn't sure how to integrate the 1/cos^2(x)

Isn't that a standard integral?? Check https://www.physicsforums.com/library.php?do=view_item&itemid=58

(and remind that $\sec^2(x)=\frac{1}{\cos^2(x)}$)

 

[crybllrd]

Wow, see what happens when I take a summer off?
Thanks a lot.