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

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

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

I=int(2x-1-x^(2))/((1+x^(2))^(2))dx is equal to

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

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

I=int((2x^(2)+1))/((x^(2)-4)(x^(2)-1))dx

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

If I_(1)=int_(e)^(e^(2))(dx)/(ln x) and I_(2)=int_(1)^(2)(e^(x))/(x)dx

(i) int((x^(2) - 1)/(x^(2) + 1))dx , (ii) int ((x^(6)- 1)/(x^(2) + 1))dx (iii) int ((x^(4))/(1+x^(2)))dx , (iv) int((x^(2))/(1+x^(2)))dx