Question

integrate 1/((x^5)*sqrt(9*x^2-1))

Answer 1

I've gotten pretty far I think,

set x= 1/3 sec(U)

Answer 2

then I got to the point where I had
\[81 \int\limits_{}^{} (\cos(x))^4 dx\]

Answer 3

the I apply the reduction formula twice and sub back in values for x to get
(81/4)*(1/(3*x))^(3)*((sqrt(9 x^2-1))/(3*x))+243/(8)*(1/(3*x))*((sqrt(9 x^2-1))/(3*x))+243