Use integration by parts to evaluate the integral $\int ( 1 - x ) e ^ { x } d x$
A) $( - 2 - x ) e ^ { x } + C$
B) $( 1 - x ) e ^ { x } + C$
C) $( 2 - x ) e ^ { x } + C$
D) $( 2 + x ) e ^ { x } + C$

Question

Quizplus · Accepted Answer

Using integration by parts, let $ u = 1 - x $ and $ dv = e^x dx $. Then $ du = -dx $ and $ v = e^x $. The integral becomes $\int (1-x)e^x dx = (1-x)e^x - \int -e^x dx = (1-x)e^x + e^x + C = (2-x)e^x + C$.

Use Integration by Parts to Evaluate the Integral ∫(1−x)exdx\int ( 1 - x ) e ^ { x } d x∫(1−x)exdx

Use Integration by Parts to Evaluate the Integral $\int ( 1 - x ) e ^ { x } d x$