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

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

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integral of e^{x/y}

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

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

Solution steps

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

Apply u-substitution

: \int e^{u} y d u

= \int e^{u} y d u

Take the constant out:

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

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

Use the common integral:

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

= y e^{u}

Substitute back

u = \frac{x}{y}

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

Add a constant to the solution

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

x \to 0 - lim (\frac{8}{x} - \frac{8}{∣ x ∣})

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

\int arccos (y) d y

\int_{- 2}^{3} 2 x^{2} + 5 d x

x \to - 7 lim (\frac{1}{x + 7})