Obtain reduction formula for `l_(n)=inttan^(n)xdx`, n being a positive integer `n le 2` and deduce the value of `int tan^(6)x dx`.

Obtain reduction formula for I_(n)=int cot^(n) x dx , n being a positive integer , n ge 2 and deduce the value of int cot^(4) x dx .

Obtain reduction formula for I_(n) =int cosec ^(n) x dx, n being a positive integer, nge 2 and deduce the value of int cosec ^(5) x dx.

Obtain reduction formula for I_n = int sin^n x dx for an integer n ge 2 and deduce the value of int sin^4 x dx .

Prove that 2^(n) gt n for all positive integers n.

If n is a positive integer then 11^n-10n-1 is divided by

Solve (x - 1)^n =x^n , where n is a positive integer.

Obtain reduction formula for If I_(n)=int (log x) ^(n)dx, then show that I_(n) =x (log x)^(n) -nI_(n-1), and hence field int (log x) ^(4) dx.