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It is given that `int(f(x))/(x^(2)(1+x)^(2))dx` is a rational function. <br> `thereforef(x)=ax^(2)+b(x+1)^(2)` . . . (i) <br> It is also given f(0) =1 and f(-1)=4. <br> `rArr1=band4=a` <br> Substituting the values of a and b in (i) , we obtain `f(x)=4x^(2)+(x+1)^(2)` <br> `rArrf(10)=4xx10^(2)+(10+1)^(2)0=521`.