`int((cosx)^(n-1))/((sinx)^(n+1))dx=` (A) `-cot^n x/n+c` (B) `-cot^n x/(n+1)+c` (C) `cot^n x/n+c` (D) `cot^n x/(n+1)+c`

If n(ne 1) in N and I_(n) = intcot^(n) x dx then I_(n) + (cot^(n-1)x)/(n-1)

If I_n = int cot^n xdx then (cot^(n - 1))/(n - 1) equals

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 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 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

int_(n in N)(a*x^(n-1))/(bx^(n)+c)dx where a,b,c are real nuber

If I=int ((((sinx)^n-sinx)^(1/n) cosx)/((sinx)^(n+1) )) dx is eqaul to (a) (n/(n^2-1))(1-1/(sinx^(n-1)))^(1/n+1)+c (b) (n/(n^2+1))(1-1/(sinx^(n-1)))^(1/n+1)+c (c) (n/(n^2+1))(1-1/(sinx^(n-1)))^(1/n)+c (d) (n/(n^2-1))(1-1/(sinx))^(1/n+1)+c

If I=int (((sinx)^n-sinx^(1/n))/((sinx)^(n+1) cosx)) dx is eqaul to (a) (n/(n^2-1))(1-1/(sinx^(n-1)))^(1/n+1)+c (b) (n/(n^2+1))(1-1/(sinx^(n-1)))^(1/n+1)+c (c) (n/(n^2+1))(1-1/(sinx^(n-1)))^(1/n)+c (d) (n/(n^2-1))(1-1/(sinx))^(1/n+1)+c

If I_(n) = int_((pi)/(4))^((pi)/(2)) cot^(n) x dx , prove that I_(n) + I_(n-2) = (1)/(n-1)

f (n) = cot ^ (2) ((pi) / (n)) + cot ^ (2) backslash (2 pi) / (n) + ............ + cot ^ (2) backslash ((n-1) pi) / (n), (n> 1, n in N) then lim_ (n rarr oo) (f (n)) / (n ^ (2)) is equal to (A) (1) / (2) (B) (1) / (3) (C) (2) / (3) (D) 1, (n> 1, n in N)