how to integrate ln(x) with respect to x?
To integrate ln(x) with respect to x, you can use integration by parts. The formula for integration by parts is ∫u dv = uv - ∫v du.
Let u = ln(x) and dv = dx. Then, du = 1/x dx and v = x.
Now apply the formula for integration by parts:
∫ln(x)dx = x ln(x) - ∫x(1/x)dx
∫ln(x)dx = x ln(x) - ∫dx
∫ln(x)dx = x ln(x) - x + C
Therefore, the integral of ln(x) with respect to x is x ln(x) - x + C, where C is the constant of integration.