Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hi,

    If I wanted to integrate e^3x-1 dx how would I go about it? I get confused when integrating e^of something.

    Also, how would I evaluate (integral)(pi/4 to 0) sin(2x+pi/4)?? I'm slightly confused with the pi part and the bit in the bracket.

    When differentiating (1-cosx)/(1+cosx) is the answer -cos2x + sin2x/sin^2x??
    When integrating (5)/(2x+3)^4 dx is the answer -(5)/(6)(2x+3)^3 + c??

    Thanks for all your help.
    Offline

    11
    ReputationRep:
    Well for the first question use the substitution u=3x. Then du/dx = 3 and therefore du/3 = dx. Substitute the dx for du/3 and the 3x for u. Now integrate with respect to u, noting that the integral of e^u is just e^u. Substitute u for 3x. You should get (1/3)*e^3x-x+c. Try this for the second integral using a different substitution.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Can someone please help me with the other questions please, I need someone to check if I have done them correct. Also, i'm still don't understand how to integrate (integral)(pi/4 to 0) sin(2x+pi/4). I know that the sin will be -cos?? and the 2x will be x^2??

    Thanks once again!
    Offline

    0
    ReputationRep:
    (Original post by FutureMedic)
    the 2x will be x^2??
    no

    have you seen this before?

    \mathrm{\displaystyle\int sin(ax+b)\ dx=-\frac{1}{a}cos(ax+b)+constant}

    this is the case a=2, b=pi/4
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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