integration challenge?

Question

the curve y(1)= [1 / (x+1) ]^n (

is reflected through the y-axis to form curve y(2) so that y(1) and its mirror image y(2) form a cusp at x=0.

curve y(2) is translated to the right a distance d to form curve y(3)
curve y(1) is translated to the right a distance d to form curve y(4)
so that y(3) and its mirror image y(4) form a cusp at x = d.

Let F = intgegral of the product, y(1)*y(3).dx over the interval 0 < x < d

Let G = integral of the product, y(1)*y(4).dx over the interval d < x < infinity

what is the value of d when F=2*G if n=1?
what is the value of d when F=2*G if n=2?
in general?

show how you got your answer.

no
no Dr R. way off! in the first place you haven't even looked at the question sufficiently to include "d" integrating the portion of the product 1/(d+1-X) between the limits 0...d

and in anycase the simple integration of the equation stated on the first line would not have the coefficient 1/(x+1) raised to the n-th power in the denominator.

Answer 1

1/((n+1)(x+1)^n+1)
You do the limits