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Exercises 4.2 Exercise

1.

Find the integration of
  1. \(\sin x \cdot \sin(\cos x)\)
    put \(\cos x =t\)
  2. \(\sin (ax+b) \cos(ax+b)\)
    put \(\sin(ax+b) =t\)
  3. \(\sqrt{ax+b}\)
    put \((ax+b) =t\)
  4. \(\displaystyle x\sqrt{x+2}\)
  5. \(\displaystyle x\sqrt{1+2x^2}\)
  6. \(\displaystyle (4x+2) \sqrt{x^2+x+1}\)
  7. \(\displaystyle \frac{1}{x-\sqrt{x}}\)
  8. \(\displaystyle \frac{x}{\sqrt{x+4}}; \, x \gt 0.\)