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    I'm stuck on the following question:

    Find the following integrals:
    c) sec^2 2x (1+sin2x) dx
    = (sec^2 2x + sec^2 2x sin2x) dx
    = (sec^2 2x + sec2x tan2x) dx
    = 0.5tan2x + 0.5sec2x + C

    The problem I have is I don't understand how I'm supposed to get from sec^2 2x sin2x to sec2x tan2x
    The question is here if it's easier to read

    https://e1934e482e1b0d2c8580c3a986eb...EZ3UTQ/CH6.pdf

    Exercise B Question 2c
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    (Original post by JW22)
    I'm stuck on the following question:

    Find the following integrals:
    c) sec^2 2x (1+sin2x) dx
    = (sec^2 2x + sec^2 2x sin2x) dx
    = (sec^2 2x + sec2x tan2x) dx
    = 0.5tan2x + 0.5sec2x + C

    The problem I have is I don't understand how I'm supposed to get from sec^2 2x sin2x to sec2x tan2x
    The question is here if it's easier to read

    https://e1934e482e1b0d2c8580c3a986eb...EZ3UTQ/CH6.pdf

    Exercise B Question 2c
    \sec^2 2x = \frac{1}{\cos^2 2x}

    So \displaystyle \sin 2x \sec^2 2x = \frac{\sin 2x}{\cos^2 2x} = \frac{\sin 2x}{\cos 2x} \times \frac{1}{\cos 2x}

    Now use the fact that \tan 2x = \frac{\sin 2x}{\cos 2x} and \sec 2x = \frac{1}{\cos 2x}
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    (Original post by JW22)
    I'm stuck on the following question:

    Find the following integrals:
    c) sec^2 2x (1+sin2x) dx
    = (sec^2 2x + sec^2 2x sin2x) dx
    = (sec^2 2x + sec2x tan2x) dx
    = 0.5tan2x + 0.5sec2x + C

    The problem I have is I don't understand how I'm supposed to get from sec^2 2x sin2x to sec2x tan2x
    The question is here if it's easier to read

    https://e1934e482e1b0d2c8580c3a986eb...EZ3UTQ/CH6.pdf

    Exercise B Question 2c
    For the first one split the fraction up into 2 separate fractions. Each of these fractions can then be integrated just by considering standard results.
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    integrate cosec^22xcot2x (cosec squared 2x multiplied by cotx)
    If you have the c4 book it's Ex 6E Q2b

    I'M VERY VERY CONFUSED
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    (Original post by habzi)
    integrate cosec^22xcot2x (cosec squared 2x multiplied by cotx)
    If you have the c4 book it's Ex 6E Q2b

    I'M VERY VERY CONFUSED
    Try u = cosec^2 2x.
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    (Original post by Zacken)
    Try u = cosec^2 2x.
    substitution method right?
    I did and for some reason I can't get to the answer! *help*
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    (Original post by habzi)
    I did and for some reason I can't get to the answer! *help*
    I think Zacken meant u = cosec2x
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    (Original post by habzi)
    substitution method right?
    I did and for some reason I can't get to the answer! *help*
    (Original post by TeeEm)
    I think Zacken meant u = cosec2x
    Nope, u = cosec^2 2x, since du/dx = -4 cot 2x cosec^2 2x which cancels nicely in the integrand.
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    (Original post by Zacken)
    Nope, u = cosec^2 2x, since du/dx = -4 cot 2x cosec^2 2x which cancels nicely in the integrand.
    I am sorry about my limitations ...
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    but the answer is supposedly -1/4cot^2 2x
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    (Original post by habzi)
    but the answer is supposedly -1/4cot^2 2x
    Yes, I get that too! Why don't you post a new thread, tag me on it and put up a picture of your working so I can see where you're going wrong?
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    (Original post by habzi)
    integrate cosec^22xcot2x (cosec squared 2x multiplied by cotx)
    if you have the c4 book it's ex 6e q2b

    i'm very very confused
    what is this omfg it looks like a massive leap from AS 😔😁
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    (Original post by RueXO)
    what is this omfg it looks like a massive leap from AS 😔😁
    Please try not to bump old threads like that
    Spoiler:
    Show
    It's not a huge leap, dw
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    (Original post by RueXO)
    what is this omfg it looks like a massive leap from AS 😔😁
    As above, refrain from necroposting. :-)
 
 
 
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