# Thread: Integration by Substitution!!

1. ## Integration by Substitution!!

(d)

i need some help with this one please..

2. $u = 4+ x^{2}$
$du = 2xdx \quad \Rightarrow \quad {\color{blue}\frac{du}{2} = x dx}$

Substitute in:
$\int \frac{{\color{blue}\frac{du}{2}}}{u^{2}} = \frac{1}{2} \int \frac{du}{u^{2}}$

3. Originally Posted by o_O
$u = 4+ x^{2}$
$du = 2xdx \quad \Rightarrow \quad {\color{blue}\frac{du}{2} = x dx}$

Substitute in:
$\int \frac{{\color{blue}\frac{du}{2}}}{u^{2}} = \frac{1}{2} \int \frac{du}{u^{2}}$

i dont quite understand, can you please show how to do the entire thing thanks

mathlete

4. What don't you understand? The last integral should be a standard one: $\int x^{n} dx = \frac{x^{n+1}}{n+1} + C \quad x\neq -1$

Here you have n = -2 ...

5. Originally Posted by o_O
What don't you understand? The last integral should be a standard one: $\int x^{n} dx = \frac{x^{n+1}}{n+1} + C \quad x\neq -1$

Here you have n = -2 ...
but can you show me the answer please geez

6. ??? You just simply apply what I told you and you're done.

We are generally here to help you through a question. It's up to you to understand what's going on and figure how to reach the end by yourself. Why don't you actually do the work and we'll see if you did it correctly or not? "geez"