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Popular Calculus >

integral of 2ye^{-x}

Solution

\int 2 y e^{- x} d y

Solution

e^{- x} y^{2} + C

Solution steps

\int 2 y e^{- x} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 e^{- x} \cdot \int y d y

Apply the Power Rule

= 2 e^{- x} \frac{y ^{2}}{2}

Simplify

2 e^{- x} \frac{y ^{2}}{2} : e^{- x} y^{2}

= e^{- x} y^{2}

Add a constant to the solution

= e^{- x} y^{2} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 2ye^{-x} ?
The integral of 2ye^{-x} is e^{-x}y^2+C