Find the Integral of 1/x

Integral represents one of the basic relationships between logarithmic and exponential functions. It is widely used to solve problems involving growth and decay, or in any situation where rates of change are inversely proportional to the quantity itself.

Answer: The integral of 1/x is ln |x| + C.

To find the integral of 1/x ​, we can use the logarithmic rule for integration. The integral of 1/x​ is represented as:

∫1/x dx

Using the rule, we get:

∫1/ x dx = ln |x| + C

,where ln represents the natural logarithm and C is the constant of integration.

This integral represents the family of functions whose derivative is 1/x​. The absolute value ∣x∣ is used because the natural logarithm is only defined for positive values of x, so it accommodates both positive and negative values of x. The constant C accounts for the fact that there are infinitely many antiderivatives of 1/x​, each differing by a constant.

Hence, the integral of 1/x is ln |x| + C.