Integration - Integrable Forms of Trigonometric Functions

Integration - Integrable Forms of Trigonometric Functions

TGM Original Questions

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

  1. \({\displaystyle\displaystyle\int 2\pi \sin \left( \frac{2ex+3}{4} \right) \mathrm{d}x}\)
  2. \({\displaystyle\displaystyle\int\frac{5-37x}{37x} \ \mathrm{d}x}\)
  3. \({\displaystyle\int(3+x)\frac{7(3+x)+4}{(3+x)} \ \mathrm{d}x}\)

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Answer:(a) \(-\dfrac{4\pi}{e}\cos\left(\dfrac{2ex+3}{4}\right)+C\); (b) \(\dfrac5{37}\ln\left|x\right|-x+C\); (c) \(\dfrac72x^2+25x+C\)

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