Integral rational function

  • #1

Homework Statement


evaluate the integral.


Homework Equations



[itex]\displaystyle\int {\frac{1}{secx+tanx} dx}[/itex]

The Attempt at a Solution


can i just do ln|secx + tanx| ??
 

Answers and Replies

  • #2
SammyS
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Homework Statement


evaluate the integral.

Homework Equations



[itex]\displaystyle\int {\frac{1}{secx+tanx} dx}[/itex]

The Attempt at a Solution


can i just do ln|secx + tanx| ??
Probably not.

What's the derivative of ln|secx + tanx| ?

Added in Edit:

Write the tangent in terms of sine & cosine and the secant as the reciprocal of the cosine.
 
Last edited:
  • #3
33,722
5,418

Homework Statement


evaluate the integral.


Homework Equations



[itex]\displaystyle\int {\frac{1}{secx+tanx} dx}[/itex]

The Attempt at a Solution


can i just do ln|secx + tanx| ??
No. You're making the same mistake you made in this thread: https://www.physicsforums.com/showthread.php?t=678488.

It is NOT TRUE that
$$ \int \frac{dx}{f(x)} = ln|f(x)| + C$$

The above is true only if f(x) = x, which is certainly not the case here.
 

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