7.1 Integration By Parts/51b: Difference between revisions
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\begin{aligned} | \begin{aligned} | ||
u &= \ln^{2}{x} \quad dv=dx \\[2ex] | u &= \ln^{2}{x} \quad dv=dx \\[2ex] | ||
du &= \frac{2}{x}\ln{x}dx | du &= \frac{2}{x}\ln{x}dx \quad v=x \\[2ex] | ||
\end{aligned} | \end{aligned} | ||
Revision as of 17:45, 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}\quad dv=dx\\[2ex]du&={\frac {2}{x}}\ln {x}dx\quad v=x\\[2ex]\end{aligned}}\end{aligned}}}