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Manipal MET2016MathematicsIndefinite Integration

The value of x+ x 3+ 2 x d x is

Options

  1. A1 4 ( 2- x+ x 2+ x- x )+C
  2. B1 2 ( 2+ x 2- x )+C
  3. C1 4 ( 1+ x 1- x )+C
  4. DNone of the above

Correct answer

A. 1 4 ( 2- x+ x 2+ x- x )+C

Step-by-step solution

Let I= x+ x 3+ 2 x d x= x+ x 4+ 2 x-1 d x I= x+ x 4-( x- x)^2 d x Put x- x=t aligned & ( x+ x) d x=d t & I= d t 4-t^2 = 1 4 2-t 2+t +C aligned = 1 4 ( 2- x+ x 2+ x- x )+C

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