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MHT CET202015 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual

e ^ x ( 1-x 1+x² )² ~d x=

Options

  1. Ae ^ x ( 1 1+x² )+ C
  2. Be ^ x ( -1 1+x² )+ C
  3. Ce ^ x ( 2 1+x² )+ C
  4. De ^ x ( -2 1+x² )+ C

Correct answer

A. e ^ x ( 1 1+x² )+ C

Step-by-step solution

aligned I &= e^ x ( 1-x 1+x² )² d x &= e^ x (1+x²-2 x ) (1+x² )² d x= e^ x [ 1+x² (1+x² )² - 2 x (1+x² )² ] d x &= e^ x [ 1 1+x² - 2 x (1+x² )² ] d x= e^ x 1+x² +C aligned

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