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• 03:12, 29 November 2022 Ricardom59381@students.laalliance.org talk contribs created page 7.1 Integration By Parts/20 (Created page with "<math> \int_{0}^{1} \left(x^{2}+1\right)e^{-x}dx </math> <math> \begin{align} u &= \ln(x)^{n} \quad dv= 1dx \\[2ex] du &=1dx \qquad v=x \\[2ex] \end{align} </math> <math> \begin{align} \int_{}^{} \left(\ln(x)^{n}\right)dx &= x \ln(x)^{n} - \int_{}^{} \left((x \frac{n \ln(x)^{n-1}}{x}) \right)dx \\[2ex] &= x \ln(x)^{n} - \int_{}^{} \left(n \ln(x)^{n-1} \right)dx \\[2ex] &= x \ln(x)^{n} - n \int_{}^{} \left(\ln(x)^{n-1} \right)dx \\[2ex] \end{align} </math>")