What is the lnx integral? Integration of ln(x)

Hello everybody. This article you can teach integral of ln(x). Now, we can go step by step of solution.

Now let's explain what the integral of lnx is with its proof.

While taking the integral, we must first convert u and dv. According to the LIATE rule, u=ln(x) and dv=dx.

>>> $du=\frac{1}{x}$ and $v=x$

1. L is Logarithmic
2. I is Inverse Trig
3. A is Algebraic
4. T is Trigonometric
5. E is Exponential

So we solving integral $\int{ln(x)dx}$ LIATE rule; $du=\frac{1}{x}$ and $v=x$

>>> $\int{ln(x)dx}=\int{udv}$

>>> $u.v=\int{vdu}$

Here we write ln(x) for u, x for v, and 1/x for du.

>>> $ln(x).x-\int{x\frac{1}{x}dx}$

>>> $ln(x).x-\int{dx}$

>>> $ln(x).x-x+C$

>>> $x.ln(x)-x$

As a result our answer, integral of ln(x) is "x.ln(x)-x"