Solve the integral of logarithmic functions int(kln(x))dx

 Exercise

$\int\left(k\ln\left(x\right)\right)dx$

 

The integral of a function times a constant ($k$) is equal to the constant times the integral of the function

$k\int\ln\left(x\right)dx$

 

The integral of the natural logarithm is given by the following formula, $\displaystyle\int\ln(x)dx=x\ln(x)-x$

$k\left(x\ln\left|x\right|-x\right)$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$k\left(x\ln\left|x\right|-x\right)+C_0$

 

Expand and simplify

$xk\ln\left|x\right|-xk+C_0$

$xk\ln\left|x\right|-xk+C_0$

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