Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    8
    ReputationRep:
    How would you integrate (e^3x +4)/e^2x ?
    Offline

    20
    ReputationRep:
    split it into two fractions & integrate them separately.
    • Community Assistant
    Offline

    21
    ReputationRep:
    Community Assistant
    You can simplify the term by cancelling the fraction to e^x + 4, as e^3x/e^2x = e^x. The rest of it can be solved by substitution.
    Offline

    20
    ReputationRep:
    (Original post by Kallisto)
    You can simplify the term by cancelling the fraction to e^x + 4, as e^3x/e^2x = e^x. The rest of it can be solved by substitution.
    I don't think you can do that. (e^3x + 4) / e^2x = e^x + 4e^-2x.
    • Community Assistant
    Offline

    21
    ReputationRep:
    Community Assistant
    (Original post by TheMindGarage)
    I don't think you can do that. (e^3x + 4) / e^2x = e^x + 4e^-2x.
    I guess I have misunderstand the fraction term. So the power is e^3x + 4 and not e^3x as I thought?
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by CelaenSardothien)
    How would you integrate (e^3x +4)/e^2x ?
    The answer on the book said (e^x)-(2e^-2x)+c but I not sure how you get to the final answer
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Kallisto)
    I guess I have misunderstand the fraction term. So the power is e^3x + 4 and not e^3x as I thought?
    (e^(3x) +4)/e^2x

    It is e to the power of 3x + 4 divide by e to the power of 2x
    Offline

    20
    ReputationRep:
    (Original post by CelaenSardothien)
    The answer on the book said (e^x)-(2e^-2x)+c but I not sure how you get to the final answer
    See what I did - split it into two powers of e. Then integrate each one separately. You'll have to either do the inverse chain rule by inspection or use substitution.
    • Community Assistant
    Offline

    21
    ReputationRep:
    Community Assistant
    (Original post by CelaenSardothien)
    (e^(3x) +4)/e^2x

    It is e to the power of 3x + 4 divide by e to the power of 2x
    So the bold print is the power. I guess I got it now. As the bear said, you should make two fractions of the term first: e^(3x) + 4/e^2x = (e^3x/^e^2x) + (4/e^2x).

    So we got what TheMindGarage simplified: e^x + 4e^-2x. Now you can integrate separetedly as the bear said as well. For 4e^-2x, you have to substitute. For substitution, you can the ignore the factor 4. You multiply the integrated term of e^-2x with 4 as last step.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 24, 2018
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.