# Thread: Fundamental Theorum of Calculus: Evaluate Indefinate Integral

1. ## Fundamental Theorum of Calculus: Evaluate Indefinate Integral

= Integral from 1 to 4: 3/(2x+1)^2
= Integral from 1 to 4: 3(2x+1)^-2

now how do I find the anti-derivative of that so that I can find F(4)-F(1)??

2. Yop,

Make appear the derivative of 2x+1

Then, the antiderivative of $u'(x) u^n(x)$ is $\frac{u^{n+1} (x)}{n+1}$

Do you understand ? Or do you need me to show ?

3. i'm still not sure, would you mind showing me?

4. $3(2x+1)^{-2}=\frac{3}{2} \underbrace{2}_{u'(x)} \underbrace{(2x+1)}_{u(x)} \ ^{-2}$

So using the formula i gave you, the antiderivative will be :

$\frac{3}{2} \frac{u^{n+1} (x)}{n+1}=\frac{3}{2} \frac{(2x+1)^{\overbrace{-2+1}^{-1}}}{-2+1}=\frac{-3}{2(2x+1)}$

Is it better ?

5. infinately!! thanks so much!!!!