1. ## Integration by Substitution!!

(d)

i need some help with this one please..

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

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

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

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

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: $\displaystyle \int x^{n} dx = \frac{x^{n+1}}{n+1} + C \quad x\neq -1$

Here you have n = -2 ...

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

Here you have n = -2 ...