Find the integral of ∫1/(1+tanx)dx

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SUMMARY

The integral of ∫1/(1+tanx)dx can be solved using various methods, including substitution and half-angle identities. The substitution method involves letting u = tan(x), while the half-angle approach utilizes the identity for tan(x - a). Both methods are valid and can yield the correct solution, demonstrating the versatility of integration techniques in calculus.

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Homework Statement
my teacher told me to solve this one in all the possible ways . I seem to have missed out on any one of them. Please help me oout
Relevant Equations
All standard integrals and concepts covered in AP calculus
I have done one by assuming tanx as u in substitution
 
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Rhdjfgjgj said:
Homework Statement: my teacher told me to solve this one in all the possible ways . I seem to have missed out on any one of them. Please help me oout
Relevant Equations: All standard integrals and concepts covered in AP calculus

I have done one by assuming tanx as u in substitution
Please show us. Thanks.
 
What is all possible ways? I can think of only substitution, but not the one you attempted. I think a half-angle should be better.
 
Also consider \tan(x - a) = \frac{\tan x - \tan a}{1 + \tan x \tan a}<br /> = \frac{1}{\tan a} - \left(\frac{1}{\tan a} + \tan a\right) \frac{1}{1 + \tan x \tan a}<br /> for suitable a.
 
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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