Integrate log x
Integration is an inverse process of differentiation. It is a process to find the area below any complex curve.
Answer: The integration of log x is x logx – x + C
Let us see, how to solve.
Use the integration by part formula, ∫uv dx = u∫v dx - ∫(du/dx ∫ v dx)dx, to calculate the integration of the logarithmic function, log x
Here, u = log x and v = 1
∫(logx.1)dx = logx∫1.dx – ∫[d(logx)/dx ∫1dx]dx
∫logx.dx = logx.(x) − ∫x.1/x dx
∫logx.dx = logx.(x) − ∫dx
∫logx.dx = xlogx – x+C
Here C is a constant