7.1 Integration By Parts/51b: Difference between revisions
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\begin{aligned} | \begin{aligned} | ||
u & = \ln^{2}{(x)} & dv &= dx \\[0.6ex] | u & = \ln^{2}{(x)} & dv &= dx \\[0.6ex] | ||
du & = \tfrac{2 | du & = \tfrac{2\ln{(x)}{x}}dx & v &= x | ||
\end{aligned} | \end{aligned} | ||
} | } | ||
Revision as of 17:51, 29 November 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \text{Use exercise 47 to evaluate} \int(\ln{x})^3dx }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \text{Exercise 47: } x(\ln{x})^n-n\int(\ln{x})^{n-1}dx }
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int \ln(x)^{3}dx&=x\ln(x)^{3}-3\underbrace {\int \ln(x)^{2}dx} _{\begin{aligned}u&=\ln ^{2}{(x)}&dv&=dx\\[0.6ex]du&={\tfrac {2\ln {(x)}{x}}{d}}x&v&=x\end{aligned}}\end{aligned}}}