" 31."(i)int(1)/((x^(2)+1)(x^(2)+4))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

Evaluate: (i) int((x^(3) + 4x^(2) -3x -2))/((x+2)) dx , (ii) int((x^(4) +1)/(x^(2) +1))dx

Evaluate: (i) int(1)/(sqrt(1+4x^(2)))dx (ii) int(1)/(sqrt(a^(2)+b^(2)x^(2)))dx

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

Evaluate: (i) int(a^(x))/(sqrt(1-a^(2x)))dx (ii) int(2x)/(sqrt(1-x^(2)-x^(4)))dx

Evaluate: (i) int(1)/(a^(2)x^(2)-b^(2))dx (ii) int(x^(2)-1)/(x^(2)+4)dx

If I_(1)= int Sin^(-1)((2x)/(1+x^(2)))dx,I_(2)= int Cos^(-1)((1-x^(2))/(1+x^(2)))dx, I_(3)= intTan^(-1)((2x)/(1-x^(2)))dx then the value of I_(1)+I_(2)-I_(3)=

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

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