Techniques of Integration · Integration by Parts
Integration by Parts
The reverse of the product rule. Choose u and dv from the integrand using the LIATE mnemonic (Logarithmic, Inverse trig, Algebraic, Trig, Exponential).
- 2 worked examples
- 16 in Techniques of Integration
Worked examples
- u = x, dv = eˣ dx → du = dx, v = eˣ
- uv - ∫ v du = xeˣ - ∫ eˣ dx = xeˣ - eˣ + C
Answer: eˣ(x - 1) + C
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Related formulas
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Common questions
What is the Integration by Parts?
The reverse of the product rule. Choose u and dv from the integrand using the LIATE mnemonic (Logarithmic, Inverse trig, Algebraic, Trig, Exponential). It is one of the techniques of integration formulas in the CalcRef reference.
How do you use the Integration by Parts?
Worked example. Find ∫ x eˣ dx. u = x, dv = eˣ dx → du = dx, v = eˣ. uv - ∫ v du = xeˣ - ∫ eˣ dx = xeˣ - eˣ + C. Answer: eˣ(x - 1) + C.
Practice
Quiz yourself on Techniques of Integration
Integration by Parts is one of 16 Techniques of Integration formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.