We can rewrite it like this#f(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)#