What is the integral of yze^{xyz} ?

The integral of yze^{xyz} is e^{yzx}+C

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integral of yze^{xyz}

\int yz e^{x yz} d x

e^{yz x} + C

Solution steps

\int yz e^{x yz} d x

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = yz x

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

Simplify

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

= e^{yz x}

Add a constant to the solution

= e^{yz x} + C