Integration - Integration of Power Functions

Integration - Integration of Power Functions

TGM Original Questions

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

  1. \(\displaystyle\displaystyle\int \frac{x^2+2x+5}{(x+1)^3}\,\mathrm{d}x\)
  2. \(\displaystyle\displaystyle\int \frac{\sqrt{5-x}+7}{\sqrt{5-x}}\,\mathrm{d}x\)

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Answer:(a) \(\ln\left|x+1\right|-\dfrac{2}{(x+1)^2}+C\); (b) \(x-14\sqrt{5-x}+C\)

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