Use integration by parts to evaluate .

Name: Use integration by parts to evaluate .
Brand: Quizplus
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Question

Use integration by parts to evaluate  . ​

Quizplus · Accepted Answer

We can use integration by parts with u = x and dv = e^x dx. Then du = dx and v = e^x.

Using the formula for integration by parts,

∫x e^x dx = x e^x - ∫e^x dx

= x e^x - e^x + C

where C is the constant of integration. Thus,

∫(x + 1) e^x dx = ∫x e^x dx + ∫e^x dx

= x e^x - e^x + e^x + C

= x e^x + C

Therefore, our answer is

11ea984b_b066_6138_9029_3102e8ae1fba_TB4005_11

Use Integration by Parts to Evaluate