How to Integrate Fractions with Substitution?

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To integrate the expression (5x-6)²/x^(1/2), substitution is a common approach, but it requires careful setup. Initially, the attempt at substitution with u=5x-6 was not effective due to improper setup. Factoring the numerator or expanding it into three terms can simplify the integration process. Ultimately, expanding the numerator made the integration straightforward. The discussion highlights the importance of choosing the right method for integration.
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Homework Statement


Integrate: (5x-6)2/x1/2


Homework Equations





The Attempt at a Solution


I tried substitution, letting u=5x-6 and then plugging that in but realized that I didn't have the proper set up for that. I'm unsure how to go about this; should I factor out the numerator or would that only make things more difficult?
 
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Multiply (5x-6)^2 out and separate the equation into three terms.
 
Expand the numerator and then it should be easy.
 
It was very easy indeed. thanks.
 

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