" 12,"f(" i) "int(x)/((x-1)^(2)(x+2))dx

I=int(1-x^(2))/(x(1-2x))dx

(i) int 1/((x^2+1)(x^2+4)) dx (ii) int 1/((x^2+1)(x^2+2)) dx

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=

If inte^(2x)f'(x)dx=g(x) , then int[e^(2x)f(x)+e^(2x)f'(x)]dx=

If inte^(2x)f'(x)dx=g(x) , then int[e^(2x)f(x)+e^(2x)f'(x)]dx=

If I_(1) = int_(0)^(1) 2^(x^(2))dx, I_(2) = int_(0)^(1) 2^(x^(3))dx , I_(3) = int_(1)^(2) 2^(x^(2))dx, I_(4)=int_(1)^(2) 2^(x^(3))dx then

(i) int_1^2 (dx)/((x+1)(x+2)) (ii) int_1^2 (x+3)/(x(x+2) dx

The number of positive continuous f(x) defined in [0,1] for with I_(1)=int_(0)^(1)f(x)dx=1,I_(2)=int_(0)^(1)xf(x)dx=a , I_(3)=int_(0)^(1)x^(2)f(x)dx=a^(2) is /are

Consider the integral I=int(xe^(x))/((1+x)^(2))dx What is the value of inte^(x)(f(x)+f'(x))dx ?