Integration - Integration of Power Functions

Integration - Integration of Power Functions

TGM Original Questions

Integrate the following expressions with respect to \(x\).

  1. \({\displaystyle\displaystyle\int \left( \frac{5}{(6x+3)^4} \right)^2 \ \mathrm{d}x}\)
  2. \({\displaystyle\displaystyle\int (2x + \sqrt{x^5})(2x - \sqrt{x^5}) \ \mathrm{d}x}\)

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Answer:(a) \(-\dfrac{25}{42(6x+3)^7}+C\); (b) \(\dfrac{4}{3}x^3-\dfrac{1}{6}x^6+C\)

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