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

I=int(1)/(x^(2))sin[(1)/(x)]dx

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

(i) int(1)/((1+x^(2))tan ^(-1) x )dx " "(ii) int(e^(tan^(-1)x))/(1+x^(2))dx

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

(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))dx

(i) int(tan^(-1))/((1+x^(2)))dx" "(ii) int(1)/(sqrt(1-x^(2)) sin^(-1)x)dx

Evaluate: (i) int(x^2+3x-1)/((x+1)^2)\ dx (ii) int(2x-1)/((x-1)^2)\ dx

Evaluate I = int_1^2 (x)/((x+1)(x+2)) 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^(3))dx then

Let I_1=int_0^1e^(x^2)dx and I_2=int_0^(1)2x^(2)e^(x^2)dx then the value of I_1 +I_2 is equal to