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• 19:10, 26 August 2022 Dvaezazizi@laalliance.org talk contribs protected 5.5 The Substitution Rule/30 [Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite) (hist)
• 19:02, 26 August 2022 Dvaezazizi@laalliance.org talk contribs created page 5.5 The Substitution Rule/30 (Created page with "<math> \int \frac{\sin{\ln{(x)}}}{x}dx </math> <math> \begin{align} u &=2+x^4 \\[2ex] du &= 4x^3dx \\[2ex] \frac{1}{4}du &= x^3dx \end{align} </math> <math> \begin{align} \int x^3(2+x^4)^5dx &= \int (x^3dx)(2+x^4) = \int \left(\frac{1}{4}du\right)(u) = \frac{1}{4}\int u\,du \\[2ex] &= \frac{1}{4} \left[\frac{u^{1+1}}{1+1}\right] + C = \frac{u^2}{8} + C \\[2ex] &= \frac{(2+x^4)^2}{8} + C \end{align} </math>")