The probability that the electron will be found within a spherical volume of radius 3a needs to be determined ( a is a constant).

The probability function is:

The integration by parts formula is given as

To integrate this function, Consider u = x² and
dv = e^-2x/adx. Then du = 2xdx and v = -a/2e^-2x/a

Use integration by parts again to determine the second term of the above expression.

Let u = x and dv = e^-2x/adx, then du = dx and
v = -a/2e^-2x/a
     

Substituting this expression into the expression of P(r) gives

Therefore,

      P(3a) = 1 - (18 + 6 +1)e^-6 = 0.938

That means the electron has 93.8% chance to be found within a sphere of 3a radius.