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

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

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

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

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

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

Evaluate : (i) int_(0)^(1)sin^(-1)xdx , (ii) int_(1)^(2)(lnx)/(x^(2))dx , (iii) int_(0)^(1)x^(2)sin^(-1)xdx .

Evaluate following : (i) inte^(x){sinx+cosx}dx (ii) inte^(x)(x^(2)+1)/((x+1)^(2)}dx

If I_(1)=int_(e)^(e^(2))(dx)/(lnx) and I_(2) = int_(1)^(2)(e^(x))/(x) dx_(1) then

If I_(1)=int_(0)^(2pi)sin^(3)xdx and I_(2)=int_(0)^(1)ln((1)/(x)-1)dx , then

The value of the integral I=int_(1)^(oo) (x^(2)-2)/(x^(3)sqrt(x^(2)-1))dx , is