I=int(1)/(x^(3)(1-x))dx

I=int(1)/(x^(3)+x^(2)+x+1)dx

Evaluate : I= "int(x^2)/((x^(3)-1))dx

Integration of rational functions I=int(x dx)/(x^(3)+1).

Let I=int_(1)^(3)|(x-1)(x-2)(x-3)|dx The value of I^(-1) .

Let I=int_(1)^(3)|(x-1)(x-2)(x-3)|dx. The value of I^(-1) .

l_(1)=int_(0)^(1)3^(x^(2))dx,l_(2)=int_(0)^(1)3^(x^(3))dx,l_(3)=int_(1)^(2)3^(x^(2))dx,l_(4)=int_(1)^(2)3^(x^(3))dx then (i)I_(1)>I_(2)(ii)I_(2)>I_(1)(iii)I_(3)>I_(4)(iv)I_(4)>I_(3)

Let I_(1)=int_(1)^(2)(x)/(sqrt(1+x^(2)))dx and I_(2)=int_(1)^(2)(1)/(x)dx .Then

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

(i) int(1)/((1+cos2x))dx , (ii) int (1)/((1-cos2x)) dx