The integral ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x , is equal to

The integral ∫2x12+5x9x5+x3+13dx, is equal to
  1. x52x5+x3+12+c
  2. -x102x5+x3+12+c
  3. -x5x5+x3+12+c
  4. x102x5+x3+12+c

Solution

Given, I=∫2x12+5x9x5+x3+13dx

=∫2x12+5x9dxx151+1x2+1x53

=∫2x3+5x6dx1+1x2+1x53

Let, 1+1x2+1x5=t ⇒-2x3-5x6dx=dt

⇒2x3+5x6dx=-dt

I=-∫dtt3=12 . t2

I=1211+1x2+1x52+c=12x10x5+x3+12+c
Where c is the constant of integration.
=x102x5+x3+12+c

Asked in: JEE Main 2016 (03 Apr)

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