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# How do you integrate x^2 / (x^3 + 2) ? watch

1. I'm going through the core 3 specimin paper as I'm retaking the exam this summer and on my teachers workthrough of the question she integrates the equation in the title as 1/3 ( ln(x^3 + 2) ). What happend to the x in the x^2? I got it as x^3 /3 ( ln(x^3 + 2) ).

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2. Use integration by substitution, setting u = x^3 +2. That simplifies it nicely, so the integrand is easy to evaluate, and it'll pop out exactly as your teacher has said! Hope this helps.
3. (Original post by mattjpye)
Use integration by substitution, setting u = x^3 +2. That simplifies it nicely, so the integrand is easy to evaluate, and it'll pop out exactly as your teacher has said! Hope this helps.
But the numerator is a derivative of the denominator, so all the OP has to do is adjust for the the by putting the 1/3 in.
4. If you haven't done integration by substitution, notice that the top is (sort of) the derivative of the bottom. This happens when differentiating ln(f(x)). So d(ln(x^3+2)/dx is equal to 3x^2/(x^3 +2). In your example the top isn't quite the derivative of the bottom, but if you imagine 3*1/3 x^2 on the top the 3's will cancel and you will get 1/3ln(x^3 +2)+c. To check your answer is right you can always differentiate this using the chain rule. Good luck in C3 in summer
5. Ah! Thank you all! I have done all this, I just forgot about it, this is the first time I've picked p core 3 since the exam so a few things have slipped my mind, thanks.

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Updated: March 30, 2013
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