The integral of ln(x) is equal to xln(x) − x + C, where C is the constant of integration.
To solve an integral with a logarithm, use the integration by parts method, where u = ln(x) and dv = dx. Then use the formula ∫u dv = uv - ∫v du to find the integral.
Yes, you can use substitution to solve an integral with ln(x). For example, if the integral is ∫ln(x) dx, you can substitute u = ln(x) and du = dx/x to get ∫u du, which can then be easily solved.
The domain of ln(x) is all positive real numbers. In other words, x must be greater than 0 for ln(x) to be defined.
No, the integral of ln(x) is not the same as the natural logarithm of x. The integral of ln(x) is a function that represents the area under the curve of ln(x), while the natural logarithm of x is a function that represents the inverse of the exponential function e^x.