[" If "lim_(a rarr oo)(1)/(a)int_(0)^(oo)(x^(2)+ax+1)/(1+x^(4))tan^(-1)((1)/(x))dx" is equal "],[" to "(pi^(2))/(k)" where "k in N" equals "]

If lim_(a rarr infty) (1)/(a)int_(0)^(infty)(x^(2)+ax+1)/(1+x^(4)). "tan"^(-1)((1)/(x))dx is equal to (pi^(2))/(K), where K in N, then K equals to

int_(0)^(oo)(tan^(-1)x)/(1+x^(2))dx

If lim_(a->oo) 1/a int_0^(oo) (x^2+ax+1)/(1+x^4) . tan^(-1) (1/x) dx is equal to pi^2/k, wherek in N equals to (A) 8 (B) 16 (C) 32 (D) 48

lim_(n rarr oo)(n)/(2^(n))int_(0)^(2)x^(n)dx equals

lim_(x rarr oo)((pi)/(2)-tan^(-1)x)^((1)/(x)) is equal to

int_(0)^(oo)((tan^(-1)x)/((1+x^(2))))dx

lim_(x rarr oo) (int_(0)^(2x) xe^(2)dx)/(e^(4x^(2))) equals :

lim_(n rarr oo) 1/n^(3) sum_(k=1)^(n) k^(2)x =

lim_(x rarr oo)tan^(-1)(x^(2)-x^(4))

The value of lim_(a rarr oo)(1)/(a^(2))int_(0)^(a)ln(1+e^(x))dx equals