Is my integral correct?

Hi so just wanted to clarify that this...

$[br]\int cos(x) +\dfrac{x^2 +1}{x}[br]$

Can integrate to...

$[br]sin(x) + (x^2 +1) \ln |x| + c[br]$

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

Hi so just wanted to clarify that this...

$[br]\int cos(x) +\dfrac{x^2 +1}{x}[br]$

Can integrate to...

$[br]sin(x) + (x^2 +1) \ln |x| + c[br]$

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

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...

$[br]n \ln |denom| [br]$

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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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!

Hi so just wanted to clarify that this...

$[br]\int cos(x) +\dfrac{x^2 +1}{x}[br]$

Can integrate to...

$[br]sin(x) + (x^2 +1) \ln |x| + c[br]$

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

Hi so just wanted to clarify that this...

$[br]\int cos(x) +\dfrac{x^2 +1}{x}[br]$

Can integrate to...

$[br]sin(x) + (x^2 +1) \ln |x| + c[br]$

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