Problem

Evaluate the integral. $ \displaystyle \int \f…

04:00

Problem 71 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{e^{2x}}{1 + e^x}\ dx $

Answer

$$e^{x}-\ln \left(1+e^{x}\right)+C$$

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Discussion

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Video Transcript

Let's try to use a use for this one. Let's take you to be either the ex deal also even X then here. So firstly, for under the use of all, rewrite this. Yeah, So you can see here. That is our to you. So we have you have here one plus you down there. And then we also see this. This is just our do you. So it's already there. So the next step here would be to do polynomial division. So go ahead and do your division here. You could do synthetic if you need to. Quotient is one and then the remainder is minus one. So we write in this form Integrate this and then finally easier use up toe back. Subutex. We could drop the absolute value here since eat of the X Plus one is positive and that's your final answer.

JH

J H.

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Top Calculus 2 / BC Educators

Grace H.

Numerade Educator

Heather Z.

Oregon State University

Samuel H.

University of Nottingham

Michael J.

Idaho State University