Rewrite the integral
Integration by parts replaces an integral of u dv with uv minus an integral of v du. The goal is to choose factors that make the new integral easier.
Calculus / English
Integration by Parts... How? (NancyPi)
NancyPi · YouTube · 17:59
YouTube · NancyPiOriginal video
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Apply integration by parts by choosing factors deliberately and using LIATE as a guide rather than a law.
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1:30Rewrite the integral7:30A polynomial times an exponential13:30Use a heuristic thoughtfullyLearning script
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Integration by parts replaces an integral of u dv with uv minus an integral of v du. The goal is to choose factors that make the new integral easier.
For xeˣ, choose and dv=eˣdx, so du=dx and ˣ. The result is xeˣ−eˣ+C, verified by differentiation.
LIATE suggests which factor to differentiate, but is not an absolute rule. Check whether the proposed dv can be integrated and whether the resulting integral is simpler; repeated applications may be needed.
Knowledge cards
A polynomial times an exponential
For xeˣ, choose and dv=eˣdx, so du=dx and ˣ. The result is xeˣ−eˣ+C, verified by differentiation.
Use a heuristic thoughtfully
LIATE suggests which factor to differentiate, but is not an absolute rule. Check whether the proposed dv can be integrated and whether the resulting integral is simpler; repeated applications may be needed.
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- Integration by parts ExplanationAt 1:30
Why this connection?
Integration by parts replaces an integral of u dv with uv minus an integral of v du. The goal is to choose factors that make the new integral easier. For xeˣ, choose and dv=eˣdx, so du=dx and ˣ. The result is xeˣ−eˣ+C, verified by differentiation. LIATE suggests which factor to differentiate, but is not an absolute rule. Check whether the proposed dv can be integrated and whether the resulting integral is simpler; repeated applications may be needed.
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A different approach
YouTube8:34Lecture for Integration by parts, compared with the current whiteboard.
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YouTube8:53Visual explanation for Integration by parts, compared with the current whiteboard.
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