00:01
In this question here we have to solve the integral part.
00:04
Integrate root x square minus 64 divided by x raised to the power 4 dx.
00:12
Here we have integrate by the part integrate by parts like integrate f g dash equals to f g minus integrate f dash g.
00:29
So here we have f is equals to under root x square minus 64 and g dash is equals to 1 upon x 4.
00:41
So here we are solving f is here and g is here.
00:47
So here first we have f dash is equals to x upon under root x square minus 64 and g dash is equals to minus 1 upon 3 x cube.
01:04
So here we are integrating we have equals to minus under root x square minus 64 divided by 3 x cube.
01:17
So minus integrate minus 1 upon 3 x square under root x square x square minus 64 dx.
01:29
Now here we are solving it then we have equals to integrate minus 1 upon 3 x square under root x square minus 64 dx.
01:44
Here we are applying the linearly so equals to minus 1 upon 3 integrate 1 upon x square root x square minus 64 dx.
01:57
Now here we have it is equals to under root 1 upon x square under root x square minus 64 dx.
02:09
Performing trigonometric substitution here substitute x is equals to 8 sec u.
02:18
Here u is equals to sec 8 upon sorry sec x upon 8 dx.
02:30
Here we have 8 sec u tan u du...