(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the indefinite integral:

2. Relevant equations

[tex]\int\frac{6}{x\sqrt{25x^2-1}} dx[/tex]

3. The attempt at a solution

I've tried a number of different substitutions, but this last one gets me the closest, I think.

[tex]\int\frac{6}{x\sqrt{25x^2-1}} dx = \frac{6}{5}\int\frac{1}{x\sqrt{x^2-\frac{1}{25}}} dx = \frac{6}{5}\int\frac{x}{x^2\sqrt{x^2-\frac{1}{25}}} dx[/tex]

let [tex]u=\sqrt{x^2-\frac{1}{25}[/tex]

then

[tex]du=\frac{x dx}{\sqrt{x^2-\frac{1}{25}}}}}[/tex]

This is where I want to substitute in, but it doesn't go. [tex]\frac{x}{\sqrt{x^2-\frac{1}{25}}}}}}dx[/tex] fits in, except for the x^2 in the denominator which doesn't work with my substitution. I don't see where to go from here, or what I should have done differently.

Thanks!

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# Homework Help: Calc II: Integration problem

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