The integral of 1/x can be computed using basic rules of calculus. Specifically, the result is:
∫ (1/x) dx = ln|x| + C
Where ln denotes the natural logarithm, |x| indicates the absolute value of x, and C is the constant of integration.
To understand why this is the case, we can look at the derivative of ln|x|. From calculus, we know that the derivative of ln|x| is:
d/dx (ln|x|) = 1/x
This means that when you integrate 1/x, you essentially reverse the process of differentiation, leading to the natural logarithm function. The absolute value is necessary because the natural logarithm function is defined only for positive values of x, but the integral of 1/x can be valid for both positive and negative values of x, which is why we include |x|.
In conclusion, the integral of 1/x is an important result in calculus, widely used in various fields such as mathematics, physics, and economics.