The integral ∫(1+x-x-1)ex+x-1dx equals to
(1+x)ex+x-1+C
(x-1)ex+x-1+C
-xex+x-1+C
xex+x-1+C
Explanation for correct option
∫(1+x-x-1)ex+x-1dx
⇒∫1+x-1xex+1xdx⇒∫ex+1xdx+∫x-1xex+1xdx⇒xex+1x-∫1-1x2ex+1xdx+∫x-1xex+1xdx⇒xex+1x-∫x-1xex+1xdx+∫x-1xex+1xdx⇒xex+1x+C⇒xex+x-1+C
Hence, option D is correct.