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In choosing \( u \) for integration by parts, the ILATE order puts first the

  • A.algebraic function
  • B.trigonometric function
  • C.inverse trigonometric function
  • D.exponential function

Answer: C

ILATE ranks inverse trigonometric, logarithmic, algebraic, trigonometric and exponential, and the earlier of the two factors is taken as \( u \). The point is that inverse and logarithmic functions simplify sharply on differentiating but are awkward to integrate, so they belong in the part that gets differentiated

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