Solving Improper Integral: \int \frac{dx}{(ax+b)^2}

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SUMMARY

The discussion focuses on solving the improper integral \(\int \frac{dx}{(3x+1)^2}\). The user seeks assistance in finding the integral of the general form \(\int \frac{dx}{(ax+b)^2}\). A key solution technique mentioned is the substitution \(u=ax+b\), which simplifies the integration process. The user successfully resolves their query with this substitution method.

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Hi, for some reason I can't remember and I've been looking everywhere for some info but can't find anything. I am trying to find out the answer to :

\int_1^i^n^f^i^n^i^t^e \frac{1}{(3x+1)^2}dx

what is the integral of \int \frac{dx}{(ax+b)^2}?

Thanks
 
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Try the substitution u=ax+b.
 
ahhh, got it, THanks
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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