The integral ∫ d x x 2 x 4 + 1 3 4 equals to

The integral ∫dxx2x4+134 equals to

  1. -x4+1x414+c
  2. x4+1x414+c
  3. x4+114+c
  4. -x4+114+c

Solution

I=∫dxx2x4+134

  =∫dxx51+1x434

Put,   1+1x4=t⇒-4x5dx=dt

∴    I=14∫-dtt34

= - 1 4 × ∫ t - 3 4 dt =-14t1414+c

=-1+1x414+c, where c is the constant of integration.

Asked in: JEE Main 2015 (04 Apr)

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