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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int e^{u} x d u

= \int e^{u} x d u

Take the constant out:

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

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

Use the common integral:

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

= x e^{u}

Substitute back

u = \frac{y}{x}

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

Add a constant to the solution

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

f (x) = 9 - ln (x), at x = 1

\int \frac{1}{x 25 x ^{2} + 1} d x

f (x) = x^{- 3}

\frac{d}{d x} (5 sin (7 x))

\int (- y^{2} + 1) - (2 y^{2} - 2) d y

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