Integral of (2x)/(x^2 + 1)

  • Thread starter ZedCar
  • Start date
  • #1
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Homework Statement



Integrate (2x)/(x^2 + 1)

Homework Equations





The Attempt at a Solution



Is the answer:

(2x) log|x^2 + 1|

as I thought the answer to this type of question is the log of the absolute value of the denominator multiplied by the numerator.

The answer given when I use Wolfram Alpha is log(x^2+1) + (tan x)^-1
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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Actually your answer would be ln(x2+1)+C. (look at putting t=x2+1)

Which is what wolfram gave to me.
 
  • #3
354
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Thank you.
Yes, I'm getting the same answer as you now on Wolfram.

If the question had instead been
Integrate (2)/(x^2 + 1) (no x in the numerator)

Would the answer also have been log|x^2 + 1| + c
 
  • #4
354
1
Oh, it's ok, I've just realised I can't do that.
 
  • #5
rock.freak667
Homework Helper
6,230
31
Thank you.
Yes, I'm getting the same answer as you now on Wolfram.

If the question had instead been
Integrate (2)/(x^2 + 1) (no x in the numerator)

Would the answer also have been log|x^2 + 1| + c
In that case the answer would be 2tan-1(x) + C since d/dx(tan-1x) = 1/(x2+1).
 

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