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• 18:23, 29 November 2022 Ricardom59381@students.laalliance.org talk contribs created page 7.1 Integration By Parts/50 (Created page with "Prove <math> \int_{}^{} \sec^{n}x = \frac{\tanx \cdot \sec^{n-2}x}{n-1} + \frac{n-2}{n-1} \int_{}^{} \sec^{n-2}xdx </math> <math> \int_{}^{} \left(\ln(x)^{n}\right)dx </math> <math> \begin{align} &u = \ln(x)^{n} \quad dv= 1dx \\[2ex] &du =1dx \quad 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(...")