7.1 Integration By Parts/31: Difference between revisions
(Created page with "<math> f'(x)= \int_{1}^{2} x^4(\ln(x))^2 \cdot dx </math> <br><br> <math>\int_{1}^{2} x^4(\ln(x))^2 \cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2}{5}\int_{1}^{2} x^4 \ln(x)\cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2x^5(\ln(x))^2}{25} + \int_{1}^{2} x^4 \cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2x^5(ln(x))^2}{25} + \frac{2x^5}{25} </math><br> <math> u= (\ln(x))^2 ~ ~ ~ ~ ~ dv=dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=\ln(x) ~ ~ ~ ~ ~ dv=x^4</m...") |
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<math> f'(x)= \int_{1}^{2} x^4(\ln(x))^2 \cdot dx </math> <br><br> | <math> f'(x)= \int_{1}^{2} x^4(\ln(x))^2 \cdot dx </math> <br><br> | ||
<math>\int_{1}^{2} x^4(\ln(x))^2 \cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2}{5}\int_{1}^{2} x^4 \ln(x)\cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2x^5(\ln(x))^2}{25} + \int_{1}^{2} x^4 \cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2x^5(ln(x))^2}{25} + \frac{2x^5}{25} </math><br> | <math>\int_{1}^{2} x^4(\ln(x))^2 \cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2}{5}\int_{1}^{2} x^4 \ln(x)\cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2x^5(\ln(x))^2}{25} + \int_{1}^{2} x^4 \cdot dx ~ ~ ~ = ~ ~ ~ \frac{x^5(ln(x))^2}{5} - \frac{2x^5(ln(x))^2}{25} + \frac{2x^5}{25} \Bigg|_1^2</math><br> | ||
<math> u= (\ln(x))^2 ~ ~ ~ ~ ~ dv=dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=\ln(x) ~ ~ ~ ~ ~ dv=x^4</math> <br> | <math> u= (\ln(x))^2 ~ ~ ~ ~ ~ dv=dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=\ln(x) ~ ~ ~ ~ ~ dv=x^4</math><br> | ||
<math> du= \frac{2}{x} \ln(x) \cdot dx ~ ~ v=x ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=\frac{1}{x} ~ ~ ~ ~ ~ v=\frac{x^5}{5}</math> <br><br> | <math>du= \frac{2}{x} \ln(x) \cdot dx ~ ~ v=x ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=\frac{1}{x} ~ ~ ~ ~ ~ v=\frac{x^5}{5}</math> <br><br> | ||
<math>=\frac{32}{5} (\ln(2))^2 -\frac{64}{25} (\ln(2)) + \frac{62}{125}</math> | <math>=\frac{32}{5} (\ln(2))^2 -\frac{64}{25} (\ln(2)) + \frac{62}{125}</math> | ||
Latest revision as of 23:03, 26 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 f'(x)= \int_{1}^{2} x^4(\ln(x))^2 \cdot dx }
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 u= (\ln(x))^2 ~ ~ ~ ~ ~ dv=dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=\ln(x) ~ ~ ~ ~ ~ dv=x^4}
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 du= \frac{2}{x} \ln(x) \cdot dx ~ ~ v=x ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=\frac{1}{x} ~ ~ ~ ~ ~ v=\frac{x^5}{5}}
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 =\frac{32}{5} (\ln(2))^2 -\frac{64}{25} (\ln(2)) + \frac{62}{125}}
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