`int(x^(1/2)+2x^(1/2)+x^(3/2)) dx `

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

int(3x^(2)+1)/((x^(2)-1)^(3))dx

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

Evaluate int(x^(2)+2x-1)/(2x^(3)+3x^(2)-2x)dx

int(x^(2)+3x-1)/((x+1)^(2))dx

int(dx)/((x+1)^(3/2)(x-1)^(1/2))

int(x^(3)+2)/((x-1)(x-2)^(3))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 and I_(4)=int_(1)^(2) 2^(x^(2))dx then