What is the integral of yze^{xy} ?

The integral of yze^{xy} is ze^{yx}+C

Popular >

integral of yze^{xy}

\int yz e^{x y} d x

z e^{y x} + C

Solution steps

\int yz e^{x y} d x

Take the constant out:

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

= yz \cdot \int e^{y x} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= yz \frac{1}{y} e^{u}

Substitute back

u = y x

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

Simplify

yz \frac{1}{y} e^{y x} : z e^{y x}

= z e^{y x}

Add a constant to the solution

= z e^{y x} + C

y = x, (4, 2)

\int \frac{4 x ^{2} + 5 x + 4}{( x ^{2} + 1 ) ^{2}} d x

\int 2 sin (x) + sin (2 x) d x

\frac{d}{d x} (1 - \frac{1}{x ^{2}})

\frac{d y}{d x} = \frac{x ^{2} + y ^{2} + x y}{x ^{2}}