Why not using the facts ?
Second question
I am supposed to integrate this question by using trig substitution
Integrate
dx/(x^2 * (x^2 + 1) ^1/2)
So I made my triangle, (x^2 + 1) is the hypotenuse, x 1 is adjacent to theta, and x is oposite of theta. Theta = to one angle
So
Tan (theta) = x/1 so
x= tan(theta)
dx = sec^2 theta
sec (theta) = (x^2 + 1)^1/2
So for my substituted integral I get
(sec(theta))^2/[(tan(theta))^2(sec(theta))]
So I get the one sec(theta) to cancel and I am left with
(sec(theta))/[((tan(theta))^2]
i can't seem to integrate it from there. I tried different trig identies, but nothing is working out.
Thanks