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AP EAMCET202017 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual

Solve (I_n+n I_ n-1 ), if (I_n= ( x)^n d x )

Options

  1. A(x( x)^ n-1 +k )
  2. B(x( x)^n+k )
  3. C( ( x)^n x +k )
  4. D( ( x)^ n-1 x +k )

Correct answer

B. (x( x)^n+k )

Step-by-step solution

( aligned I_n & = ( x)^n I_n & =( x)^n d x- ( d( x)^n d x d x ) d x+k I_n & =x( x)^n- n( x)^ n-1 x x+k I_n & =x( x)^n-n I_ n-1 +k I_n & =n I_ n-1 =x( x)^n+k aligned )

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