Techniques of Integration · Integration by Parts
Tabular Method (Repeated IBP)
A shortcut for repeated integration by parts when one factor is a polynomial. Create a table of derivatives and antiderivatives with alternating signs.
- 0 variables
- 2 worked examples
- 16 in Techniques of Integration
Worked examples
Find ∫ x³ eˣ dx using the tabular method.
- Derivatives of x³: x³, 3x², 6x, 6, 0
- Integrals of eˣ: eˣ, eˣ, eˣ, eˣ
- Signs: +, -, +, -
- Result: x³eˣ - 3x²eˣ + 6xeˣ - 6eˣ + C
Answer: eˣ(x³ - 3x² + 6x - 6) + C
1 more worked examplePremium
Find ∫ x² sin x dx using the tabular method.
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Practice
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