# Thread: Integral Help - Trig

1. ## Integral Help - Trig

Integral of:

(tan(x)-1)^2

Please show major steps. I'm not understanding this. Thanks for your help.

2. Hello, mathnoob!

$\displaystyle \int (\tan x -1)^2dx$

We have: .$\displaystyle (\tan x - 1)^2\:=\:\tan^2\!x-2\tan x + 1 \:=\:(\sec^2x - 1) - 2\tan x + 1$

Then: .$\displaystyle \int\left(\sec^2\!x - 2\tan x\right)\,dx$

Can you finish it now?

3. If I split it up:

integral(sec(x)^2)dx - integral(2tan(x))dx

I don't know the integral for sec(x)^2. I do know sec(x), however. That is ln(sec(x)+tan(x)).

Can this help somehow?

4. I don't know the integral for sec(x)^2. I do know sec(x), however. That is ln(sec(x)+tan(x)).
You do know this. What is the derivative of tan x?

You do know this. What is the derivative of tan x?
The derivative of tan(x) is sec(x)^2.

6. Originally Posted by mathnoob
The derivative of tan(x) is sec(x)^2.

What's with the confused emoticon ....???

If the derivative of tan x is sec^2(x), then clearly the integral of sec^2(x) is tan x.

7. Oh boy.

8. integral(sec(x)^2)dx - integral(2tan(x))dx

tan(x) + C1 + 2ln(cos(x)) + C2

tan(x) + 2ln(cos(x)) + C

Is this right? This isn't what my TI-89 is giving me.

9. Originally Posted by mathnoob
integral(sec(x)^2)dx - integral(2tan(x))dx

tan(x) + C1 + 2ln(cos(x)) + C2

tan(x) + 2ln(cos(x)) + C

Is this right? This isn't what my TI-89 is giving me.
that's correct. what does your calculator give you?

10. Originally Posted by mathnoob
integral(sec(x)^2)dx - integral(2tan(x))dx

tan(x) + C1 + 2ln(cos(x)) + C2

tan(x) + 2ln(cos(x)) + C

Is this right? This isn't what my TI-89 is giving me.
It's probably giving you some weird and wonderful answer that is equivalent to tan(x) + 2ln(cos(x)) + C. You can easily check your by-hand answer ...... differentiate it!! You should get the integrand back .....