∫[xe^(arctanx)/(1+x^2)^(3/2)]dx =∫[xe^(arctanx)/(1+x^2)^(3/2)]d(arctanx) =∫[x/(1+x^2)^(1/2)]d[e^(arc

∫[^()/(1+x^2)^(3/2)]dx =∫[xe^(arctanx)/(1+x^2)^(3/2)]d(arctanx) =∫[x/(1+x^2)^(1/2)]d[e^(arctanx)] =[x/(1+x^2)^(1/2)]e^(arctanx)-∫[1/(1+x^2)^(1/2)]d[e^(arctanx)/(1+x^2)^(3/2)]dx =[x…