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

Problem

(∫_^)(1/(1+y2)*d(y))

Solution

1. Identify the integrand as a standard form from the table of basic integrals.

2. Recognize that the derivative of the inverse tangent function, arctan(y) is exactly 1/(1+y2)

3. Apply the rule for the antiderivative of 1/(1+y2) which results in the inverse tangent function plus a constant of integration.

Final Answer

(∫_^)(1/(1+y2)*d(y))=arctan(y)+C

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