Use integration by parts to evaluate . Note that evaluation may require integration by parts more than once.

Question

Use integration by parts to evaluate  . Note that evaluation may require integration by parts more than once. ​

Quizplus · Accepted Answer

Let u = x and dv = e^(x/2)dx. Then du/dx = 1 and v = 2e^(x/2). Using integration by parts, we get:
∫x e^(x/2)dx = uv - ∫vdu/dx dx 
= 2xe^(x/2) - ∫2e^(x/2) dx 
= 2xe^(x/2) - 4e^(x/2) + C 
= 2e^(x/2)(x - 2) + C
So the answer is 11eb0d3b_98a6_5096_9790_790bb773a869_TB1243_11.

Use Integration by Parts to Evaluate