Integration By Parts
Using integration by parts, ∫x·eˣ dx equals
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About This Question
- Subject
- mathematics
- Chapter
- integral calculus
- Topic
- integration by parts
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
xeˣ - eˣ + C
- Rule: ∫udv=uv−∫vdu.
- Choice of variables: Use LIATE rule.
- Let u=x (algebraic) ⟹du=dx
- Let dv=exdx (exponential) ⟹v=ex
- Substitution:
- ∫xexdx=(x)(ex)−∫exdx
- =xex−ex+C
- Simplification: ex(x−1)+C.
This medium difficulty mathematics question is from the chapter integral calculus, covering the topic of integration by parts. It appeared in the 2025 exam.
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