Evaluating the Integral Using Trig Substitution

[cmantzioros]

The question is to evaluate the integral in the attachment.

Using trig substition, I've reduced it to ∫ (tanz)^2 where z will be found using the triangle. I just need to integrate tangent squared which I can't seem to figure how to do. I tried using the trig identity (secx)^2 - 1 but I don't know what to do after.

 

[arildno]

That is a good move.

Hint:
What do you get if you differentiate tan(z)?

 

[cmantzioros]

I get (sec(z))^2)

 

[arildno]

That is to integrate tan, I said differentiate it!

 

[cmantzioros]

Yes, sorry I realized I had made a mistake so when I differentiate tan, I get sec^2 ...

 

[arildno]

Indeed, so therefore you DO know an anti-derivative for sec^2, don't you?

Therefore, you should be able to find an anti-derivative for tan^2(z)=sec^2(z)-1

 

[cmantzioros]

So simple... thanks a lot