The integral of 1/x is log x + C.

Let's understand the solution in detail.

Explanation:

We know that,

d/dx[ ln(x)] =1 / x

Thus, we will do the counter process here to find the integral of 1/x

Hence, the integral of 1/x is given by the loge|x| which is the natural logarithm of absolute x also represented as or ln x.

Note: We can't use the integral identity for xn here, since ∫xn dx = xn + 1/(n + 1) + C, and here, for 1/x, we have n = -1. Hence, ∫x-1 dx = x0/0 = undefined.

Also, we add a constant C to it if it's an indefinite integral.

By specifying the limits of the integral we can find its specific value.

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