Solving the Integral ∫(1/x)dx | Step-by-Step Solution using Basic Integration Rule for Natural Logarithms

∫(1/x)dx

To solve the integral ∫(1/x)dx, we can use the basic integration rule for natural logarithms

To solve the integral ∫(1/x)dx, we can use the basic integration rule for natural logarithms. The integral of 1/x with respect to x is ln|x| + C, where C is the constant of integration.

Here’s the step-by-step solution:

1. Start with the integral: ∫(1/x)dx.

2. Recognize that 1/x can be written as x^(-1). So, we have ∫(x^(-1))dx.

3. Apply the power rule of integration, which states that ∫(x^n)dx = (x^(n+1))/(n+1), where n is any real number except -1. Applying this rule, we get ∫(x^(-1))dx = (x^0)/(0) = ln|x| + C.

4. Don’t forget to include the constant of integration (C) in the answer. This is because when we integrate, we lose information about any constant term in the original function.

Therefore, the solution to the integral ∫(1/x)dx is ln|x| + C.

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