Evaluate the Integral integral of 5/(x^2+1) with respect to x

Problem

(∫_^)(5/(x2+1)*d(x))

Solution

1. Identify the constant factor in the integrand and move it outside the integral.

(∫_^)(5/(x2+1)*d(x))=5*(∫_^)(1/(x2+1)*d(x))

2. Recognize the standard integral form for the inverse tangent function, where (∫_^)(1/(x2+1)*d(x))=arctan(x)

(∫_^)(1/(x2+1)*d(x))=arctan(x)

3. Apply the result of the standard integral and include the constant of integration C

5*(∫_^)(1/(x2+1)*d(x))=5*arctan(x)+C

Final Answer

(∫_^)(5/(x2+1)*d(x))=5*arctan(x)+C

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