Integration - Integration of Power Functions

Integration - Integration of Power Functions

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

  1. \(10x^4 - 5x^2 + x + 3\)
  2. \(6\sqrt[3]{x} - \frac{2}{\sqrt{x}} + 8x^3\)
  3. \(\frac{4\sqrt[5]{x} + 3x^4 + \sqrt{x}}{6x^3}\)

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Answer:(a) \(2x^5-\frac53x^3+\frac12x^2+3x+C\). (b) \(\frac92x^{4/3}-4x^{1/2}+2x^4+C\). (c) \(-\frac{10}{27}x^{-9/5}+\frac14x^2-\frac19x^{-3/2}+C\).

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