What is the integral of (yze^{xyz}) ?

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

Popular >

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

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

= 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

\int cos (r) r d r

\int x e^{x^{2}} (1 + x^{2}) d x

\int cos^{4} (x) sin^{1} (x) d x

\int \frac{25 x}{4 3 x ^{2} + 4} d x

\int \frac{2 x}{5 x ^{2} - 5} d x