1. ## Integration by subtitution

Use the substitution $x=tan\theta$ to find the exact value of

$
\int{\frac{1-x^2}{1+x^2}}dx$

limits root 3 and 1

I know, that when you sub you have to change the limits:
$root 3=tan\theta$
$\theta=\frac{pi}{4}$

$1=tan\theta$
$\theta=\frac{pi}{4}$

Please show me how to do this.
Thanks

2. $
\int{\frac{1-x^2}{1+x^2}}dx$

limits root 3 and 1

Please show me how to do this.
Thanks[/quote]
x = tanθ
Then dx = sec^2(θ)*d(θ)
When x = 1, θ = Π/4
When x = sqrt(3), θ = π/3
The given integration becomes
int[(1-tan^2θ)/(1+tan^2θ)*sec^2(θ)*d(θ)
That reduces to
int[(1-tan^2(θ)*d(θ) between π/4 to π/3.
Put tan^2(θ) = sec^2(θ) - 1 and solve the integration.

3. Thats really helpful so far, but i can't remember how to integrate that. any hel there?

4. What is the integration of sec^2(x)?

5. oh yh, im being silly.