Integrate secx(tanx - secx) dx

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The integral of secx(tanx - secx) dx is evaluated as secxtanx - sec^2x dx. The solution simplifies to secx - tanx + C. The initial integration approach is confirmed to be correct. The discussion focuses on the integration process and verification of the solution.
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Homework Statement


Integrate...
secx(tanx - secx) dx


The Attempt at a Solution


secxtanx - sec^2x dx =

secx - tanx + C

is that right?
 
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it is correct
 
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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