00:01
All right, so because we have a minus sign here and the x squared is first, i know that this is a second substitution.
00:09
And then the way i think about it is i need this to have a 25 in the front of it.
00:17
So i need 4x squared to be 25 secant squared theta.
00:23
That way, 4x squared minus 25 turns into the square root of 25 secant squared theta, minus 25.
00:34
Then i can factor that 25 out.
00:41
So that gives me the square root of 25 tangent squared, which is 5 tangent theta.
00:50
Okay.
00:51
And then in place of x, well, i'm going to have to solve this for x here.
00:57
So i have 2x equals 5 secant.
01:03
So x is 5 over 2 secant theta, which is what they said to use for substitution, but that's why.
01:12
And then dx is five halves, secant tangent theta, d theta.
01:20
Seekin theta, tangent theta, d theta.
01:26
Okay.
01:28
So this integral turns into five tangent theta.
01:35
That's what the square root is equal to.
01:38
Then dx, which is this, five halves, secant theta, tangent theta, d theta, over x, which is five halves, secant theta, d theta.
01:58
Okay, so the five halves and the five halves, oh, no d theta there.
02:03
Five halves secant theta...