7.1 Integration By Parts/4: Difference between revisions
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<math>du = dx \qquad v = -e^{-x}</math> | <math>du = dx \qquad v = -e^{-x}</math> | ||
<math>\int (xe^{-x}) dx = x(-e^{-x}) - \int (-e^{-x}) | <math>\int (xe^{-x}) dx = x(-e^{-x}) - \int (-e^{-x}) = -xe^{-x}-\int (-e^{-x})dx</math> | ||
</math> | |||
<math>=-xe^{-x}+\int (e^{-x})dx = -xe^{-x}-e^{-x}+C</math> <br><br> | |||
<math>=-e^{-x}(x+1)+C</math> | |||
Latest revision as of 03:02, 29 November 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int (xe^{-x})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 = x \qquad dv = e^{-x}}
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 = dx \qquad v = -e^{-x}}
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 \int (xe^{-x}) dx = x(-e^{-x}) - \int (-e^{-x}) = -xe^{-x}-\int (-e^{-x})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 =-xe^{-x}+\int (e^{-x})dx = -xe^{-x}-e^{-x}+C}
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 =-e^{-x}(x+1)+C}