Integration with Eulers formula.

Click For Summary
SUMMARY

The discussion centers on integrating the function \(\frac{e^x}{\cos(x)}\) using Euler's formula. The user begins by rewriting the expression as \(\frac{e^x}{e^{ix}}\) and proceeds to integrate, resulting in \(\frac{e^{(1-i)x}}{1-i}\). The conversation highlights the method of multiplying by the complex conjugate and back substituting \(e^{ix}\) to extract the real part. Participants confirm that it is valid to back substitute \(i\sin(x) + \cos(x)\) and then multiply by \((1-i)\) before taking the real part.

PREREQUISITES
  • Understanding of complex numbers and Euler's formula
  • Knowledge of integration techniques in calculus
  • Familiarity with complex conjugates and their properties
  • Ability to manipulate exponential functions
NEXT STEPS
  • Study the application of Euler's formula in complex integration
  • Learn about complex conjugates and their role in integration
  • Explore advanced integration techniques involving complex functions
  • Review real and imaginary parts of complex functions in calculus
USEFUL FOR

Mathematicians, engineering students, and anyone interested in advanced calculus and complex analysis will benefit from this discussion.

cragar
Messages
2,546
Reaction score
3
I want to integrate \frac{e^x}{cos(x)} with eulers formula.
I start by writing \frac{e^x}{e^{ix}}
then I integrate that as usual.
So after I integrate I get \frac{e^{(1-i)x}}{1-i}
Normally I would multiply and divide by the complex conjugate and then back substitute in
e^(ix) and the take the real part.

can I just back substitute in isin(x)+cos(x) on the bottom and then multiply it by (1-i)
and then take the real part. That seems to easy.
Does anyone have suggestions. This is not a homework problem.
 
Physics news on Phys.org
Hey cragar.

You should be able to integrate the expression and then take the real part as your answer.
 

Similar threads

Undergrad What Happens When You Differentiate Euler's Formula?
  • · Replies 11 ·
Replies
11
Views
7K
High School Simple Derivation Of Euler's Formula And Applications
  • · Replies 2 ·
Replies
2
Views
2K
High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
3K
Graduate How do I apply the method of steepest descents to this integral?
  • · Replies 1 ·
Replies
1
Views
3K
High School Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
High School Differentiating Euler formula vs. multiplying by i
  • · Replies 3 ·
Replies
3
Views
3K
High School Integrating sec(x): Understanding the Answer
  • · Replies 6 ·
Replies
6
Views
3K
Graduate What is the history and significance of Euler's formula?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Integral using Euler's formula.
  • · Replies 10 ·
Replies
10
Views
7K
Graduate Integration with eulers formula.
  • · Replies 1 ·
Replies
1
Views
2K