Integration by Parts: Formula, LIATE Rule and Examples
Integration by parts: ∫u dv = uv − ∫v du. How to choose u with LIATE, 6 worked examples (x·sin x, ln x, arctan x, eˣ·cos x) and the tabular method.
Tag: integration by parts
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Integral of x·e^x: Integration by Parts Step by Step
∫x·e^x dx = x·e^x − e^x + C. A clear integration by parts walkthrough with LIATE, x²e^x, x·e^(2x), x·e^(−x) and a definite integral.
Integral of ln(x): x ln x − x + C (Integration by Parts)
The integral of ln(x) is x·ln(x) − x + C. Full integration by parts derivation, a check by differentiation, definite integral examples and variations.