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FP2 Help - Integrating 1/(x(x+1))

Hi,

I have been struggling to do the integral of 1/(x(x+1)). It is part of a larger question so it can't be that hard...

I've split it into the partial fractions 1/x - 1/(x+1) but then I must integrate this. I know that the integral of 1/x = ln(x) but how do I go about the integral of 1/(x+1)?

Thank you
Integral of 1/(x+1) dx is ln(x+1) +c, c4 stuff!
Reply 2
Avatar for JM-97
JM-97
7
Original post by omarathon
Hi,

I have been struggling to do the integral of 1/(x(x+1)). It is part of a larger question so it can't be that hard...

I've split it into the partial fractions 1/x - 1/(x+1) but then I must integrate this. I know that the integral of 1/x = ln(x) but how do I go about the integral of 1/(x+1)?

Thank you


clue is, It's going to be similar to ln(x)

so we know the derivative of ln(x) is 1/x

so what can we differentiate to get 1/(x+1) ?

try ln(x+1) ?
Reply 3
Avatar for omarathon
omarathon
OP
13
Original post by black1blade
Integral of 1/(x+1) dx is ln(x+1) +c, c4 stuff!


Is this another one of those rules we just must remember?

I'm doing FP2 rn but it has C3 and C4 as assumed knowledge... I haven't completed either.
Original post by omarathon
Is this another one of those rules we just must remember?

I'm doing FP2 rn but it has C3 and C4 as assumed knowledge... I haven't completed either.


Well the rule from C3 is that ∫f′(x)f(x).dx=ln⁡∣f(x)∣+c\displaystyle \int \frac{f'(x)}{f(x)} .dx = \ln| f(x) | +c and clearly ∫1x+1dx\displaystyle \int \frac{1}{x+1}dx follows this criteria. Also you need the modulus brackets unless x>0x>0 in context.
(edited 6 years ago)
Original post by omarathon
Is this another one of those rules we just must remember?

I'm doing FP2 rn but it has C3 and C4 as assumed knowledge... I haven't completed either.


Well it's a reverse chain rule but yeah finish c3 and 4 before finishing fp2 I'd recommend.
Reply 6
Avatar for JM-97
JM-97
7
You definitely need C3 & C4 knowledge for FP2 otherwise you'll be running into 'problems' like this all the time
Reply 7
Avatar for omarathon
omarathon
OP
13
Original post by RDKGames
Well the rule from C3 is that ∫f′(x)f(x).dx=ln⁡∣f(x)∣+c\displaystyle \int \frac{f'(x)}{f(x)} .dx = \ln| f(x) | +c and clearly ∫1x+1dx\displaystyle \int \frac{1}{x+1}dx follows this criteria. Also you need the modulus brackets unless x>0x>0 in context.


Thanks that makes a lot of sense. I needed clarity on the general rule as I was just told that the integral of 1/x is ln(x), nothing else.

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