" 1) `"int(cot^(-1)x)/(1+x^(2))dx=`

int cot^(-1)(1-x+x^(2))dx

" (i) "int e^(cot^(-1)x)*(1)/(1+x^(2))dx

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

int_(0)^(1)(cot^(-1)x)/(1+x^(2))dx

int_(0)^(1)((cot^(-1)x)^(2))/(1+x^(2))dx=

int(tan^(-1)x cot^(-1)x)/(1+x^(2))dx

int_(0)^(1)cot^(-1)(1-x+x^(2))dx

int(tan^(-1)x+cot^(-1)x)/(1+x^(2))dx

If int_(0)^(1)cot^(-1)(1-x+x^(2))dx=lambda int_(0)^(1)tan^(-1)xdx, then lambda is equal to 1( b) 2(c)3(d)4

int(1+tan^(2)x)/(1+cot^(2)x)dx