# Integral rational function

## Homework Statement

evaluate the integral.

## Homework Equations

$\displaystyle\int {\frac{1}{secx+tanx} dx}$

## The Attempt at a Solution

can i just do ln|secx + tanx| ??

## Answers and Replies

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SammyS
Staff Emeritus
Homework Helper
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## Homework Statement

evaluate the integral.

## Homework Equations

$\displaystyle\int {\frac{1}{secx+tanx} dx}$

## The Attempt at a Solution

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

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

Write the tangent in terms of sine & cosine and the secant as the reciprocal of the cosine.

Last edited:
Mark44
Mentor

## Homework Statement

evaluate the integral.

## Homework Equations

$\displaystyle\int {\frac{1}{secx+tanx} dx}$

## 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.