7.1 Integration By Parts/51b: Difference between revisions

Revision as of 17:38, 29 November 2022

${\text{Use exercise 47 to evaluate}}\int (\ln {x})^{3}dx$

${\text{Exercise 47:}}\qquad x(\ln {x})^{n}-n\int (\ln {x})^{n-1}dx$

${\begin{aligned}\int \ln(x)^{3}dx=x\ln(x)^{3}-3\int \ln(x)^{2}dx\end{aligned}}$

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	<math> \text{~~use Exercise~~ 47 to evaluate} \int(\ln{x})^3dx </math> <br><br>		<math> \text{Use exercise 47 to evaluate} \int(\ln{x})^3dx </math> <br><br>
	<math> \text{Exercise 47:}\qquad x(\ln{x})^n-n\int(\ln{x})^{n-1}dx </math> <br><br>		<math> \text{Exercise 47:}\qquad x(\ln{x})^n-n\int(\ln{x})^{n-1}dx </math> <br><br>