What is the integral of 2ye^{xy} ?

The integral of 2ye^{xy} is 2(e^{xy} 1/x y-e^{xy} 1/(x^2))+C

Popular >

integral of 2ye^{xy}

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

2 (e^{x y} \frac{1}{x} y - e^{x y} \frac{1}{x ^{2}}) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: e^{x y} \frac{1}{x} y - \int e^{x y} \frac{1}{x} d y

= 2 (e^{x y} \frac{1}{x} y - \int e^{x y} \frac{1}{x} d y)

\int e^{x y} \frac{1}{x} d y = e^{x y} \frac{1}{x ^{2}}

= 2 (e^{x y} \frac{1}{x} y - e^{x y} \frac{1}{x ^{2}})

Add a constant to the solution

= 2 (e^{x y} \frac{1}{x} y - e^{x y} \frac{1}{x ^{2}}) + C

(10, 6), (- 5, - 3)

\int t^{11} e^{- t^{6}} d t

\int \frac{77}{e ^{- x} + 1} d x

x \to 0 - lim (\frac{∣ x ∣}{2 x})

\frac{d}{d x} (\frac{e ^{\frac{1}{x}}}{x})

What is the integral of 2ye^{xy} ?
The integral of 2ye^{xy} is 2(e^{xy} 1/x y-e^{xy} 1/(x^2))+C