Step 1 :Let's perform polynomial long division on the given polynomials.
Step 2 :The dividend is \(7x^{3} + x^{2} + x\).
Step 3 :The divisor is \(x^{2} + 1\).
Step 4 :Performing the division, we find that the quotient is \(7x\).
Step 5 :So, the result of the polynomial long division is \(\boxed{7x}\).