Homework Help is Here – Start Your Trial Now!
Math
Calculus
Evaluate "xp- a. Start with the substitution u = e* and note that u² = e*, This should lead to the integral [ -du. b. Next use a trig. substitution u = (trig. function of 0) (You will end up with a sin 20. To convert back to u and then x you can use sin(28) = 2sin@ cos0.)

Evaluate "xp- a. Start with the substitution u = e* and note that u² = e*, This should lead to the integral [ -du. b. Next use a trig. substitution u = (trig. function of 0) (You will end up with a sin 20. To convert back to u and then x you can use sin(28) = 2sin@ cos0.)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
Question
**Evaluate the integral** \[ \int \frac{e^x}{1-e^{2x}}\, dx. \] ### Steps to Approach the Integral **a. Start with the substitution** \[ u = e^x \] and note that \[ u^2 = e^{2x}. \] This should lead to the integral \[ \int \frac{u}{1-u^2}\, du. \] **b. Next, use a trigonometric substitution** \[ u = \text{(trig. function of } \theta \text{)} \] --- *(At this point, you will end up with a \(\sin{2\theta}\). To convert back to \(u\) and then \(x\), you can use \(\sin{(2\theta)} = 2\sin{\theta}\cos{\theta}\)).*
Transcribed Image Text:**Evaluate the integral** \[ \int \frac{e^x}{1-e^{2x}}\, dx. \] ### Steps to Approach the Integral **a. Start with the substitution** \[ u = e^x \] and note that \[ u^2 = e^{2x}. \] This should lead to the integral \[ \int \frac{u}{1-u^2}\, du. \] **b. Next, use a trigonometric substitution** \[ u = \text{(trig. function of } \theta \text{)} \] --- *(At this point, you will end up with a \(\sin{2\theta}\). To convert back to \(u\) and then \(x\), you can use \(\sin{(2\theta)} = 2\sin{\theta}\cos{\theta}\)).*
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Indefinite Integral
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS