Evaluate the Integral integral of 1/(1+x^2) with respect to x

Problem

(∫_^)(1/(1+x2)*d(x))

Solution

1. Identify the integrand as a standard form in calculus.

2. Recognize that the derivative of the inverse tangent function, arctan(x) is 1/(1+x2)

3. Apply the fundamental integration rule for this specific rational function.

4. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(1/(1+x2)*d(x))=arctan(x)+C

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