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

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

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integral of e^{x/(sqrt(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 2 lim (sin (\frac{2}{x - 2}))

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

\int - \frac{1}{2} cos (2 x) + C d x

x^{4} e^{6 x}

\frac{d ^{3} y}{d x ^{3}} + \frac{d ^{2} y}{d x ^{2}} - 2 y = 0

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