`int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdx` is equal to (a)`-pi/2lnpi` (b) 0 (c)`pi/2ln2` (d) none of these

The value of int_(-2 pi)^(5 pi)cot^(-1)(tan x)dx is equal to (7 pi)/(2)(b)(7 pi^(2))/(2)(c)(3 pi)/(2) (d) None of these

int_0^pi dx/(1-2acosx+a^2), alt1 is equal to (A) (pialog2)/4 (B) (4pi)/(2-a^2) (C) pi/(1-a^2) (D) none of these

int_(0)^(oo)(xdx)/((1+x)(1+x^(2))) is equal to (A)(pi)/(4) (B) (pi)/(2)(C)pi(D) none of thesel

int_0^(pi//2)1/(1+cot^3x)dx is equal to 0 b. 1 c. pi//2 d. pi//4

int_0^1d/(dx){sin^(-1)((2x)/(1+x^2))}dx is equal to 0 (b) pi (c) pi//2 (d) pi//4

lim_(x rarr1)(1-x^(2))/(sin2 pi x) is equal to (a)(1)/(2 pi)(b)-(1)/(pi)(c)(-2)/(pi)(d) none of these

int_(-(pi)/(2))^((pi)/(2))(e^(|sin x|)cos x)/(1+e^(tan x))dx is equal to (a) e+1 (b) 1-(pi)/(2)e(c)e-1(d) none of these

int_1^(e^(17))(pi"sin"(pi(log)_e x))/x dx is equal to (A) 2 (B) -2 (C) 2//pi (D) none of these

sqrt(3)int_0^pi dx/(1+2sin^2x)= (A) -pi (B) 0 (C) pi (D) none of these

The value of int_(-pi/2)^( pi/2)(x^(3)+x cos x+tan^(5)x+1)dx is equal to (A)0(C)pi(B)2(D) none of these (i) 0 (ii)2(iii) pi (iv) none of these