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    Hi so just wanted to clarify that this...

    

\int cos(x) +\dfrac{x^2 +1}{x}

    Can integrate to...

    

sin(x) + (x^2 +1) \ln |x| + c

    Thanks in advance, the mark scheme has something different but just like the thread earlier today I want to clarify I'm doing this right
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    (Original post by 01Chris02)
    Hi so just wanted to clarify that this...

    

\int cos(x) +\dfrac{x^2 +1}{x}

    Can integrate to...

    

sin(x) + (x^2 +1) \ln |x| + c

    Thanks in advance, the mark scheme has something different but just like the thread earlier today I want to clarify I'm doing this right
    This isn't correct, I'd separate your fraction into two separate ones and then you should be able to see your mistake


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    (Original post by 01Chris02)
    Hi so just wanted to clarify that this...

    

\int cos(x) +\dfrac{x^2 +1}{x}

    Can integrate to...

    

sin(x) + (x^2 +1) \ln |x| + c

    Thanks in advance, the mark scheme has something different but just like the thread earlier today I want to clarify I'm doing this right
    Close! Obviously the cosx is correct but you should split the fraction and try from there

    EDIT: Just seen the post above me, oops, was too late!
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    So is a general rule to fully factorize and split? Then integrate? I was differentiating then denominator and then multiplying it by a term (n) so that it gave the numerator. Then putting it in the form...

    

n \ln |denom|

    This was what my teacher had said to do! :/

    Thanks guys so far!

    EDIT: Does this only apply to making n a constant and not a variable?
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    (Original post by 01Chris02)
    So is a general rule to fully factorize and split? Then integrate? I was differentiating then denominator and then multiplying it by a term (n) so that it gave the numerator. Then putting it in the form...

    

n \ln |denom|

    This was what my teacher had said to do! :/

    Thanks guys so far!

    EDIT: Does this only apply to making n a constant and not a variable?
    Well whenever I integrate I always make sure everything is in its simplest form first and to split up fractions, unless you can see that the numerator is the derivative of the denominator, in which case you should know what it integrates to


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    (Original post by MathsNerd1)
    Well whenever I integrate I always make sure everything is in its simplest form first and to split up fractions, unless you can see that the numerator is the derivative of the denominator, in which case you should know what it integrates to


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    That's great thanks, I actually feel ready for C3 tomorrow! All past papers done now and this was the last issue I had! Thanks!
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    (Original post by 01Chris02)
    That's great thanks, I actually feel ready for C3 tomorrow! All past papers done now and this was the last issue I had! Thanks!
    Glad I could help and best of luck with your exam! If you need any more help I'll be happy to help


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    (Original post by 01Chris02)
    Hi so just wanted to clarify that this...

    

\int cos(x) +\dfrac{x^2 +1}{x}

    Can integrate to...

    

sin(x) + (x^2 +1) \ln |x| + c

    Thanks in advance, the mark scheme has something different but just like the thread earlier today I want to clarify I'm doing this right
    close but no... seperate the fraction I bet you that the ms has 0.5x^2+ln(x) where you have (x^2+1)ln(x)

    bear in mind that in your problem the top and bottom are BOTH functions of x
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    (Original post by 01Chris02)
    Hi so just wanted to clarify that this...

    

\int cos(x) +\dfrac{x^2 +1}{x}

    Can integrate to...

    

sin(x) + (x^2 +1) \ln |x| + c

    Thanks in advance, the mark scheme has something different but just like the thread earlier today I want to clarify I'm doing this right
    The first part is fine but you played an "illegal move" on the second part. The reason is that if you tried differentiating your result, you'd have to use the product rule. Like others have said, try splitting it up which would make it a lot easier

    Good luck in your exam
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    Thanks guys, you've been a big help!
 
 
 
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