let 9x^2-1 = y^2
=> 18xdx = 2ydy
=> ydy = 9xdx
lower limit = sqrt(9*2/9 - 1) = sqrt(1) = 1
upper limit = sqrt(9*4/9 - 1) = sqrt(3)
Int. [sqrt(2)/3,2/3] 1/(x^5(sqrt(9x^2-1)) dx
= Int. [sqrt(2)/3,2/3] xdx/(x^6(sqrt(9x^2-1))
= 81* Int. [1,sqrt(3)] ydy/((y^2+1)^3y)
=81* Int. [1,sqrt(3)] dy/(y^2+1)^3
y=tanz
dy = sec^2z dz
=81*Int [pi/4,pi/3] cos^4(z) dz
=81/4*int [pi/4,pi/3] (1+cos(2z))^2 dz
=81/4* Int. [pi/4,pi/3] (1+2cos(2z)+cos^2(2z)) dz
=81/4*(pi/3-pi/4) + 81/4*(sin(2pi/3)-sin(pi/2)) + 81/8 * (pi/3-pi/4)
+ 81/32 *(sin(-pi/3)-sin(pi))
=81(pi/48+pi/96+1/4*(sqrt(3)/2 - 1) - 1/32 * sqrt(3)/2)
=81/32*(pi+3sqrt(3)-8)
