If `n!=1, int_0^(pi/4) (tan^nx+tan^(n-2)x)d(x-[x])=` (A) `1/(n-1)` (B) `1/(n+1)` (C) `1/n` (D) `2/(n-1)`

If I_n=int_(pi/4)^(pi/2) (tanx)^-n dx(ngt1) , then I_n+I_(n+2)= (A) 1/(n-1) (B) 1/(n+1) (C) -1/(n+1) (D) 1/n-1

If I_n=int_0^(pi/4) tan^nx then lim_(nrarroo)n(I_n+I_(n-2)) equals (A) 1/2 (B) 1 (C) oo (D) 0

If I_(n)=int_(0)^( pi/4)tan^(n)xdx, prove that I_(n)+I_(n-2)=(1)/(n+1)

The value of int_(0)^(pi//4) (tan^(n)x+tan^(n-2)x)d(x-([x])/(1!)+([x]^(2))/(2!)-([x]^(3))/(3!)+....) where [x] is greatest function, is

The nth term of the coresponding series of int_(0)^(1)tan^(-1)xdx is (A) (pi)/(4n) (B) ((1)/(n))tan^(-1)(n-1)(C)(pi)/(2n)(D)tan^(-1)(n)

If int(tan^(2)x+tan^(4)x)dx=((1)/(n))tan^(n)x+c, then n=

Let f(x)=x/(1+x^n)^(1/n) for nge2 and g(x)=ubrace(fofo…of)_("f occurs n times")(x) . Then intx^(n-2)g(x)dx equals (A) 1/(n(n-1))(1+nx^n)^(1-1/n)+K (B) 1/(n-1)(1+nx^n)^(1-1/n)+K (C) 1/(n(n+1))(1+nx^n)^(1+1/n)+K (D) 1/(n+1)(1+nx^n)^(1-1/n)+K

Find int tan^nx sec^2x\ dx, (n!=-1)

tan {n (pi) / (2) + (- 1) ^ (n) (pi) / (4)} = 1