What is the integral from 0 to 3 of e^{x+3y} ?

The integral from 0 to 3 of e^{x+3y} is e^{3+3y}-e^{3y}

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integral from 0 to 3 of e^{x+3y}

\int_{0}^{3} e^{x + 3 y} d x

e^{3 + 3 y} - e^{3 y}

Solution steps

\int_{0}^{3} e^{x + 3 y} d x

Apply u-substitution

= \int_{3 y}^{3 + 3 y} e^{u} d u

Use the common integral:

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

= [e^{u}]_{3 y}^{3 + 3 y}

Compute the boundaries:

e^{3 + 3 y} - e^{3 y}

= e^{3 + 3 y} - e^{3 y}

What is the integral from 0 to 3 of e^{x+3y} ?
The integral from 0 to 3 of e^{x+3y} is e^{3+3y}-e^{3y}