" (r) "int_(-2)^(2)(3x^(2))/(1+e^(x))dx" equals "

Match the statements/expression given in Column I with the values given in Column II. Column I, Column II (p) The number of polynomials f(x) with non-negative integer coefficients of degree lt=2, satisfying f(0)=0 and int_0^1f(x)dx=1,i s , 8 (q) The number of points in the interval [-sqrt(13),sqrt(13)] at which f(x)=sin(x^2)+"cos"(x^2) attains its maximum value, is, 2 (r) int_(-2)^2(3x^2)/(1+e^x)dx equals, 4 (s)(int_(-2)^2cos2xdotlog((1+x)/(1-x))dx)/(int_0^ (1/2)""cos2xdotlog((1+x)/(1-x))dx) , 0

Match the statements/expression given in Column I with the values given in Column II. Column I, Column II (p) The number of polynomials f(x) with non-negative integer coefficients of degree lt=2, satisfying f(0)=0 and int_0^1f(x)dx=1,i s , 8 (q) The number of points in the interval [-sqrt(13),sqrt(13)] at which f(x)=sin(x^2)+"cos"(x^2) attains its maximum value, is, 2 (r) int_(-2)^2(3x^2)/(1+e^x)dx equals, 4 (s)(int_(-2)^2cos2xdotlog((1+x)/(1-x))dx)/(int_0^ (1/2)""cos2xdotlog((1+x)/(1-x))dx) , 0

int x^2 e^(x^3) dx equals :

int e^(x)((x^(2)-3)/((x-1)^(2)))dx is equal to

int_(-3)^(3)(x^(2))/((x^(2)+3)(1+e^(x)))dx is equal to

int_(-1)^(1)(e^(x)+e^(-x))/(2(1+e^(2x)))dx is equal to

If int_(0)^(1) (e^(x))/( 1+x) dx = k , then int_(0)^(1) (e^(x))/( (1+x)^(2)) dx is equal to

int(2)/((e^(x)+e^(-x))^(2))dx is equal to

The value of int_(-pi//2)^(pi//2) (x^(2)cos x )/(1+e^(x)) dx is equal to