How does u-substitution work: ∫ y e − y / 2 2 d y

∫ y e − y 2 d y = ∫ − 2 u e u ( − 2 d u ) = − 2 2 ∫ − u e u d u = − 2 3 2 ∫ − u e u d u .

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Jameson Lucero

2022-07-02

How does u-substitution work:

\int \frac{\sqrt{y} e^{- y / 2}}{2} d y

Kayley Jackson

Beginner2022-07-03Added 16 answers

\int \sqrt{y} e^{- \frac{y}{2}} d y = \int \sqrt{- 2 u} e^{u} (- 2 d u) = - \sqrt{2} 2 \int \sqrt{- u} e^{u} d u = - 2^{\frac{3}{2}} \int \sqrt{- u} e^{u} d u .

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