We can rewrite it like thisf(x)=e^(xln3)e^(-x+1) so that we can write inte^(xln3)e^(-x+1)dx and integrating by parts we have inte^(xln3)e^(-x+1)dx= =-e^(-x+1)e^(xln3)-int-e^(-x+1)ln3e^(xln3)dx= -e^(-x+1)e^(xln3)+ln3inte^(xln3-x+1)dx inte^(xln3-x+1)dx=e^(xln3-x+1)/(ln3-1)