Problems from Definite integral and Barrow's rule

Development:

We will proceed the following way:

• Find the primitive function of the integrand.

${\displaystyle \int (\ln (x){)}^3\cdot {\displaystyle \frac{1}{x}}dx={\displaystyle \frac{(\ln (x){)}^4}{4}}}$

• Evaluate it at the ends of the interval of integration.

$[{\displaystyle \frac{(\ln (x){)}^4}{4}}{]}_1^e={\displaystyle \frac{(\ln (e){)}^4}{4}}-{\displaystyle \frac{(\ln (1){)}^4}{4}}={\displaystyle \frac{1}{4}}-0={\displaystyle \frac{1}{4}}$

Solution:

${\displaystyle {\int }_1^e\frac{(\ln (x){)}^3}{x}dx={\displaystyle \frac{1}{4}}}$

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