ZedCar said: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
The integral of (2x)/(x^2 + 1) is ln(x^2 + 1) + C, where C is the constant of integration.
To solve this integral, you can use the substitution method by letting u = x^2 + 1. Then, du/dx = 2x and the integral becomes ∫(2x)/(x^2 + 1) dx = ∫(1/u) du = ln(u) + C = ln(x^2 + 1) + C.
The domain of this function is all real numbers, as the denominator x^2 + 1 is always positive and does not equal to 0 for any real value of x.
Yes, this integral can also be solved using the partial fractions method by breaking down the function into simpler fractions and then integrating each term separately. However, the substitution method is often easier and more efficient for this particular integral.
Since this integral does not have any specified limits of integration, it is considered an indefinite integral. This means that the result is a function, rather than a specific numerical value.