The integral \(\int \frac{1}{\sec x + \tan x} \, dx\) cannot be evaluated simply as \(\ln|\sec x + \tan x| + C\). This misconception arises from the incorrect assumption that the integral of \(\frac{1}{f(x)}\) is always \(\ln|f(x)| + C\), which only holds true when \(f(x) = x\). To correctly evaluate this integral, one must express \(\tan x\) in terms of sine and cosine and recognize that \(\sec x\) is the reciprocal of cosine.
PREREQUISITESStudents studying calculus, particularly those focusing on integral calculus, as well as educators looking to clarify common misunderstandings in evaluating integrals involving trigonometric functions.
Probably not.whatlifeforme said: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| ??
whatlifeforme said: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| ??