What is the integral of e^x(y+2z) ?

The integral of e^x(y+2z) is e^x(yz+z^2)+C

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integral of e^x(y+2z)

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

e^{x} (yz + z^{2}) + C

Solution steps

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

Take the constant out:

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

= e^{x} \cdot \int y + 2 z d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= e^{x} (\int y d z + \int 2 z d z)

\int y d z = yz

\int 2 z d z = z^{2}

= e^{x} (yz + z^{2})

Add a constant to the solution

= e^{x} (yz + z^{2}) + C

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