Question

Given the integral:

$LaTeX: \int\frac{dx}{x^5\sqrt{9x^2\:-\:1}}$ ∫ d x x 5 9 x 2 − 1

Identify the following in order to complete a trigonometric substitution:

From the radical expression, what is a? What is u?

What should the trig substitution be?

[That is, complete the appropriate substitution:

u = a $LaTeX: \cdot$ ⋅ sin( $LaTeX: \theta$ θ ), a = a $LaTeX: \cdot$ ⋅ tan( $LaTeX: \theta$ θ ), or u = a $LaTeX: \cdot$ ⋅ sec( $LaTeX: \theta$ θ )]

Do NOT compute the integral. Just identify the appropriate substitution.

Answer 1