What is the integral of e^{x+y+z} ?

The integral of e^{x+y+z} is e^{y+z+x}+C

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integral of e^{x+y+z}

\int e^{x + y + z} d x

e^{y + z + x} + C

Solution steps

\int e^{x + y + z} d x

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

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

= e^{u}

Substitute back

u = y + z + x

= e^{y + z + x}

Add a constant to the solution

= e^{y + z + x} + C

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