Math Help - Help with trig subs...

1. Help with trig subs...

i cant seem to figure out what to sub in into the integral of x/(((x+2)^2)+9). PAny help greatly apprehiated asap.... Thanks!

2. Originally Posted by skater8705
i cant seem to figure out what to sub in into the integral of x/(((x+2)^2)+9). PAny help greatly apprehiated asap.... Thanks!
$\int \frac{x}{\sqrt{(x+2)^2+9}} dx$
Let $t=x+2$ so,
$\int \frac{t-2}{\sqrt{t^2+9}} dt = \int \frac{t}{\sqrt{t^2+9}} dt - 2 \int \frac{1}{\sqrt{t^2+9}} dt$
The first integral use the substitution $\xi = t^2$ and the second is an inverse sine integral.

3. Originally Posted by skater8705
i cant seem to figure out what to sub in into the integral of x/(((x+2)^2)+9).
$\int\frac x{(x+2)^2+9}\,dx.$

Define $x+2=3\tan u\implies dx=3\sec^2u.$

Substitute and play with it.

4. thanks for the responses... both methods seemed to get the same ans... thanks again!!!