WEBVTT

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V tomto videu se ještě víc
procvičíme použití substituce,

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kdy se hodí ji použít a jak
správně definovat proměnnou "u".

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Mějme neurčitý integrál (přirozeného
logaritmu z x) na desátou,

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to celé děleno x dx.

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Hodí se použít substituci a pokud ano,
tak jak definovat proměnnou "u"?

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Klíč k úspěchu je vidět, jestli někde
ve výrazu mám funkci a také i její derivaci.

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A možná jste rovnou poznali,

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že derivace přirozeného
logaritmu z x je 1 lomeno x.

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Aby to bylo lépe,

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tak můžu tento integrál zapsat jako
(ln(x) na desátou) krát 1 lomeno x dx.

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Nyní to je vidět lépe.

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Máme funkci přirozený logaritmus z x
umocněnou na desátou,

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ale taky tady máme
její derivaci, 1 lomeno x.

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Takže můžeme použít substituci.

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Můžeme definovat "u" jako
přirozený logaritmus z x.

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Důvod, proč jsem vybral
přirozený logaritmus z x, je ten,

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že vidím tady jeho derivaci.

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A pak může říct, že
du lomeno dx je rovno 1 lomeno x.

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Což znamená, že du
je rovno 1 lomeno x dx.

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A tady to máme.

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Toto je du, a toto je naše "u".

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Krásně to zjednodušilo na
integrál z (u na desátou) du.

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