`ifint(dx)/(x^2(x^n+1)^(((n-1)/n)) )=-[f(x)]^(1/n)+c ,t h e nf(x)i s` (a)`(1+x^n)` (b) `1+x^(-1)` (c)`x^n+x^(-n)` (d) none of these

If int(dx)/(x^(2)(x^(n)+1)^((n-1)/(n)))=-(f(x))^((1)/(n))+C then f(x) is (A)1+x^(n)(B)1+x^(-n)(C)x^(n)+x^(-n)(D)x^(n)-x^(-n)

If f(x)=(a-x^(n))^((1)/(n)) then fof(x) is (A) x (B) a-x (C)x^(2)(D)-(1)/(x^(n))

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

f(x) is a continuous function for all real values of x and satisfies int_(n+1)^(n+1)f(x)dx=(n^(2))/(2)AA n in I. Then int_(5)^(5)f(|x|)dx is equal to (19)/(2) (b) (35)/(2) (c) (17)/(2) (d) none of these

int_(n)^(n+1)f(x)dx=n^(2)+n then int_(-1)^(1)f(x)dx=

int_(1/n)^((an-1)/n) sqrt(x)/(sqrt(a-x)+sqrt(x))dx= (A) a/2 (B) (na+2)/(2n) (C) (na-2)/(2n) (D) none of these

If (d)/(dx)[ x^(n+1)+c]=(n+1)x^(n) , then find int x^(n)dx .

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^(+)(x+2)^(n-3)(x+1)^(2)++(x+1)^(n)(x+2)^(n-2)-(x+1)^(n) b.(x+2)^(n-2)-(x+1)^(n-1) c.(x+2)^(n)-(x+1)^(n) d.none of these