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Popular >

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

: \frac{y ^{2}}{2}

= 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

Popular Examples

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\int \frac{3 x - 1}{x ^{2} + 2 x + 2} d x

integral of x^3(x^2-1)^{3/2}

\int x^{3} (x^{2} - 1)^{\frac{3}{2}} d x

integral of 1/(x^3+2x^2+2x)

\int \frac{1}{x ^{3} + 2 x ^{2} + 2 x} d x

integral of (xcos(x)-sin(x))/x

\int \frac{x cos ( x ) - sin ( x )}{x} d x

integral of 1/(sqrt(x^4-4x^2))

\int \frac{1}{x ^{4} - 4 x ^{2}} d x

Frequently Asked Questions (FAQ)

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