|
|
|
|
|
|
Integral of $$$\frac{1}{\ln\left(x\right)}$$$
The calculator will find the integral/antiderivative of $$$\frac{1}{\ln\left(x\right)}$$$, with steps shown.
Related calculator: Integral Calculator
Solution
This integral (Logarithmic Integral) does not have a closed form:
$${\color{red}{\int{\frac{1}{\ln{\left(x \right)}} d x}}} = {\color{red}{\operatorname{li}{\left(x \right)}}}$$
Therefore,
$$\int{\frac{1}{\ln{\left(x \right)}} d x} = \operatorname{li}{\left(x \right)}$$
Add the constant of integration:
$$\int{\frac{1}{\ln{\left(x \right)}} d x} = \operatorname{li}{\left(x \right)}+C$$
Answer: $$$\int{\frac{1}{\ln{\left(x \right)}} d x}=\operatorname{li}{\left(x \right)}+C$$$