Calculating indefinite integrals

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The discussion focuses on calculating indefinite integrals for various functions. The integrals presented include S 13(4^x + 3^x)dx, S (cosx + sec^2x)dx, S (3-(1/x))dx, and S e^(7x)dx. The initial attempts at solutions are critiqued, with corrections noted for c) and d), where the integral of "3" should be "3x" and substitution is required for d). The correct approach for d) involves letting u = 7x for integration. Overall, the conversation emphasizes the importance of proper integration techniques and corrections to initial solutions.
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Homework Statement


a) S 13(4^x + 3^x)dx
b) S (cosx + sec^2x)dx
c) S (3-(1/x))dx
d) S e^(7x)dx


Homework Equations



The S is supposed to be the integration sign

The Attempt at a Solution



Are these correct or at least close?

a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C

b) = (sinx + tanx) + C

c) = -ln + C

d) Do I use U-substitution for this one?
 
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c) and d) are incorrect. The integral of "3" is "3x". For d), yes, use substitution. Let u= 7x.
 
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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