" 12."quad (i)int(x)/((x+1)^(2))dx

Evaluate (i) int(xe^(x))/((x+1)^(2))dx (ii) int x^3e^(-x) dx

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

int(x^(6)-1)/(x^(2)+1)dx12

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

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

int_(0)^(12)(2x)dx-1=

Find int(1)/(x^(2)+4x+12)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

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

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