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

Problem

(∫_^)(2/(x2+1)*d(x))

Solution

1. Identify the constant in the numerator and move it outside the integral.

(∫_^)(2/(x2+1)*d(x))=2*(∫_^)(1/(x2+1)*d(x))

2. Recognize the standard integral form for the inverse tangent function.

(∫_^)(1/(x2+1)*d(x))=arctan(x)+C

3. Multiply the result by the constant factor of 2

2*(∫_^)(1/(x2+1)*d(x))=2*arctan(x)+C

Final Answer

(∫_^)(2/(x2+1)*d(x))=2*arctan(x)+C

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