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

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

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

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

int_(1)^(2)(3x)/(9x^(2)-1)dx

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

Evaluate : (i) inte^(x)((1)/(x)-(1)/(x^(2)))dx (ii) inte^(x)((1)/(x^(2))-(2)/(x^(3)))dx (iii) inte^(x){sin^(-1)x+(1)/(sqrt(1-x^(2)))}dx (iv) inte^(x)(tanx+logsecx)dx

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

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

Evaluate: (i) int(1)/(sqrt(x))(1+(1)/(x))dx (ii) int(x^(6)+1)/(x^(2)+1)dx

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