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

Problem

(∫_^)(1/(x+1)*d(x))

Solution

1. Identify the form of the integral, which matches the basic integration rule (∫_^)(1/u*d(u))=ln(u)+C

2. Apply the substitution u=x+1 which implies d(u)=d(x)

3. Integrate the expression with respect to u to find the natural logarithm of the absolute value of the denominator.

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

Final Answer

(∫_^)(1/(x+1)*d(x))=ln(x+1)+C

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