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

Solve the integral using trigonometric substitution.

[tex]\int[/tex][tex]\frac{\sqrt{4x^{2}+9}}{x^{4}}[/tex]dx

2. Relevant equations

2x=3tan[tex]\theta[/tex]

x=2/3 tan[tex]\theta[/tex]

dx=2/3 sec^{2}[tex]\theta[/tex]d[tex]\theta[/tex]

[tex]\sqrt{4x^{2}+9}[/tex]=3sec[tex]\theta[/tex]

3. The attempt at a solution

[tex]\frac{8}{9}[/tex] [tex]\int[/tex] [tex]\frac{cos^{2}\theta}{sin^{4}\theta}[/tex] d[tex]\theta[/tex]

From here, I don't know how to get the integral into a form that is easy to solve.

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# Homework Help: Integration by trigonometric substitution

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