What is the integral of e^{(2y)/x} ?

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

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integral of e^{(2y)/x}

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

\frac{x}{2} e^{\frac{2 y}{x}} + C

Solution steps

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

Apply u-substitution

: \int \frac{x e ^{u}}{2} d u

= \int \frac{x e ^{u}}{2} d u

Take the constant out:

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

= \frac{x}{2} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{x}{2} e^{u}

Substitute back

u = \frac{2 y}{x}

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

Add a constant to the solution

= \frac{x}{2} e^{\frac{2 y}{x}} + C

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