00:01
We'd like to evaluate the integral of the square root of x squared minus 1, all divided by x to the 4th.
00:10
So since the expression in the radical, x squared minus 1 is of the form x squared minus a squared, or a is 1, we'll use a trig substitution of this form.
00:24
So in our case, we have x equals 1 times secant, such as secan theta.
00:30
So that's our trigsub.
00:34
Taking a derivative gives us dx.
00:44
So let's plug this in.
00:48
So the integral equals.
00:51
Also, before we go on, let's evaluate x squared minus 1 inside the radical.
00:59
So this will be secant squared minus 1.
01:06
So square root of tan square theta, which is simply tan theta.
01:15
So we have a tan theta in the numerator.
01:19
So in dx becomes secan theta, tan theta...