hothien220903 hothien220903
  • 15-06-2021
  • Mathematics
contestada

[tex]\int\limits^a_b {\frac{1}{xln(x)} } \, dx[/tex]

Respuesta :

Trancescient
Trancescient Trancescient
  • 15-06-2021

Step-by-step explanation:

Let u = ln x

du = dx/x

[tex]\int {\frac{1}{x \ln(x)} }\: dx = \int \frac{du}{u}[/tex]

[tex]= \ln |u| + k[/tex]

or

[tex]\int_b^a {\frac{1}{x \ln(x)} }\:dx= \ln |\ln|x|| _b^a[/tex]

[tex]=\ln|\ln(a)| - \ln|\ln(b)|[/tex]

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