anonymous
  • anonymous
∫x+1/2x-x2+2 dx
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Pls guys help me solve this problem i have Exams tomorrow. pls
anonymous
  • anonymous
do you know how to long divide polynomials?
anonymous
  • anonymous
yes

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anonymous
  • anonymous
That's pretty much what you have to do here, so that your integral becomes (-x+3) - (1/(x+1)). Then you can solve the integral.
anonymous
  • anonymous
hold up a minute, I think I messed it up, give me a minute or two.
anonymous
  • anonymous
ok
anonymous
  • anonymous
the denominator is 2x-x square + 2
anonymous
  • anonymous
it looks like you separate by partial fractions \[x+1 =( Ax +B)/(2x-x^2+2)\]. Because the deonimator is a irreducible quadratic eq. Once you solve for A and B, then you should have a differentiable eq.
anonymous
  • anonymous
sorry about the mix up before I jumped into a bad conclusion too fast.
anonymous
  • anonymous
\[\int\limits \left(2+\frac{1}{2 x}+x-x^2\right) \, dx = 2 x+\frac{x^2}{2}-\frac{x^3}{3}+\frac{\text{Log}[x]}{2} \]
anonymous
  • anonymous
hello
anonymous
  • anonymous
is that the final ans.
anonymous
  • anonymous
from robtobey, Yes. Another version is the result factored: \[\frac{1}{6} \left(12 x+3 x^2-2 x^3+3 \text{Log}[x]\right) \]
anonymous
  • anonymous
You can check the result of the integration by taking the derivative of the result with respect to x.

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