Question
how to integrate ln(x) with respect to x?
Answers
GPT 3.5
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.
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.