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• 16:13, 14 September 2022 Ricardom59381@students.laalliance.org talk contribs created page 5.5 The Substitution Rule/37 (Created page with "<math> \int \cotx dx </math> <math> \begin{align} u &= 3ax+bx^3 \\[2ex] du &= (3a+3bx^2)dx \\[2ex] \frac{1}{3}du &= (a+bx^2)dx \\[2ex] \end{align} </math> <math> \begin{align} \int \frac{a+bx^2}{\sqrt{3ax+bx^3}}dx &= \int \frac{1}{\sqrt{3ax+bx^3}}(a+bx^2)\;dx = \int \frac{1}{\sqrt{3ax+bx^3}}(a+bx^2\;dx)\ \\[2ex] &= \frac{1}{3}\int \frac{1}{\sqrt{u}}(du) = \frac{1}{3}\int u^{-1/2} du \\[2ex] &= \frac{1}{3}\frac{u^{\frac{1}{2}}}{\frac{1}{2}} + C \\[2ex] &= \frac{...")