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

Find the integral of [tex]\int\frac{5dx}{\sqrt{25x^2 -9}}, x > \frac{3}{5}[/tex]

3. The attempt at a solution

First, I made x = 3/5 secx, and dx = 3/5 secxtanxdx

[tex]\int\frac{3secxtanxdx}{5\sqrt{(9/25)(sec^2x -1)}}[/tex]

[tex]\int\frac{secxtanxdx}{tanx}[/tex]

[tex]\int secxdx[/tex]

[tex]ln|secx + tanx| + C[/tex]

[tex]ln|\frac{5x}{3} + \frac{5\sqrt{x^2 - \frac{9}{25}}}{3}| + C[/tex]

The final step is my answer. However, when I try to integrate using the wolfram integration calculator, I get [tex]ln|2(\sqrt{25x^2 - 9} + 5x) + C[/tex]

Where did I go wrong?

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# Homework Help: Integration problem

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