What is the integral of e^{x+2y} ?

The integral of e^{x+2y} is 1/2 e^{x+2y}+C

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integral of e^{x+2y}

\int e^{x + 2 y} d y

\frac{1}{2} e^{x + 2 y} + C

Solution steps

\int e^{x + 2 y} d y

Apply u-substitution

= \int e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2} e^{u}

Substitute back

u = x + 2 y

= \frac{1}{2} e^{x + 2 y}

Add a constant to the solution

= \frac{1}{2} e^{x + 2 y} + C