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    I'm rubbish at integration by substitution and I just can't get it right! Plus I can't figure out how I've gone wrong either, if someone can figure out where I've gone wrong with this question please (I'll post my working from my phone now)

    (Integrate) 1/(cos^2x)(1+2tanx)^2 when u=1+2tanx

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    the answer is −1/(2(1+2tanx)) +c
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    (Original post by mica-lwe)
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    1/u2 does not integrate to lnu
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    Instead of writing what dx is equal to, write it as what du is equal to
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    (Original post by TeeEm)
    1/u2 does not integrate to lnu
    Is that where I've gone wrong then? Is it better to take 1/2 out the integral and integrate u^-2?
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    (Original post by mica-lwe)
    Is that where I've gone wrong then? Is it better to take 1/2 out the integral and integrate u^-2?
    sure

    then you are one step from the required answer
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    (Original post by TeeEm)
    sure

    then you are one step from the required answer
    thankyou! Have no idea why I struggle with substitution when there's harder stuff on the paper
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    (Original post by mica-lwe)
    thankyou! Have no idea why I struggle with substitution when there's harder stuff on the paper
    practice
    if this fails try practice
    and as a back up technique try practice...

    http://www.madasmaths.com/archive/ma...e_mixed_up.pdf


    http://www.madasmaths.com/archive/ma...ons_part_i.pdf
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    (Original post by TeeEm)
    practice
    if this fails try practice
    and as a back up technique try practice...

    http://www.madasmaths.com/archive/ma...e_mixed_up.pdf


    http://www.madasmaths.com/archive/ma...ons_part_i.pdf
    I'll try these, thanks!
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    (Original post by mica-lwe)
    I'll try these, thanks!
    long download time but full solutions

    all the best
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    hi,


    Your solution makes a good start... it is fine until the line =1/2 ∫ 1/(u^2) du


    keep the half outside the integral sign to simplify things; then 1/(u^2) is the same as u^(-2) because the reciprocal of a number makes the power negative and:


    ∫ u^(-2) du = -1/u +c as you divide by the power then add one to it ...don't forget the constant (c).


    so... 1/2 ∫ u^(-2) du = -1/2u +c and you can just swap u for the substitution you made at the start.


    Hope that helps
 
 
 
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