What is the integral of (e^{xy}) ?

The integral of (e^{xy}) is 1/x e^{xy}+C

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integral of (e^{xy})

\int (e^{x y}) d y

\frac{1}{x} e^{x y} + C

Solution steps

\int e^{x y} d y

Apply u-substitution

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

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

Take the constant out:

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

= \frac{1}{x} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{x} e^{u}

Substitute back

u = x y

= \frac{1}{x} e^{x y}

Add a constant to the solution

= \frac{1}{x} e^{x y} + C

(\frac{1}{tan ( x )})^{^{'}}

lo g_{5} (5 x^{3} + 2 x + 5)

y^{^{'}} = tan (t) y - 5 t

2916 x, 108 x^{2}

\frac{d}{d x} ((4 x)^{4 x})