7.1 Integration By Parts/51b: Difference between revisions
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\int\ln(x)^3dx &= x\ln(x)^3 \underbrace{ | \int\ln(x)^3dx &= x\ln(x)^3 -3\underbrace{\int\ln(x)^2dx} \\ | ||
Revision as of 17:42, 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}c&=1\\ddd&=12\\\end{aligned}}\int \ln(x)^{3}dx&=x\ln(x)^{3}-3\int \ln(x)^{2}dx\\\end{aligned}}}