What is the Integral of (2)/(x^2 + 1)?

[ZedCar]

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

 

[rock.freak667]

Actually your answer would be ln(x²+1)+C. (look at putting t=x²+1)

Which is what wolfram gave to me.

 

[ZedCar]

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

 

[ZedCar]

Oh, it's ok, I've just realized I can't do that.

 

[rock.freak667]

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).