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

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

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integral of 2e^{x/y}

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int e^{u} y d u

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

Take the constant out:

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

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

Use the common integral:

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

= 2 y e^{u}

Substitute back

u = \frac{x}{y}

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

Add a constant to the solution

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

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