[" If "int(dx)/((x+2)(x^(2)+1))=a ln(1+x^(2))+b tan^(-1)x],[+(1)/(5)ln|x+2|+C" .Then "]

If int dx/((x+2)(1+x^(2)) ) = a log(1+x^(2))+b tan^(-1)x+1/5 log (x+2)+c

" "int(log x)/((1+x)^(2))dx

int_( then )^( If )(dx)/((x+2)(x^(2)+1))=a log|1+x^(2)|+b tan^(-1)x+(1)/(5)log|x+2|+c

int(1)/(x(log x)^(2))dx

If int (2x^(2)+3)/((x^(2)-1)(x^(2)+4)) dx = a log((x-1)/(x+1)) +b tan^(-1) (x/2) +c then the values of a and b are

int_((1)/(2))^(2)(ln x)/(1+x^(2))dx

int_(x)^(1)x ln(1+2x)dx

" & "int((1+log x)^(2))/(x)dx=