What is the integral of e^{(x+3)} ?

The integral of e^{(x+3)} is e^{3+x}+C

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integral of e^{(x+3)}

\int e^{(x + 3)} d x

e^{3 + x} + C

Solution steps

\int e^{x + 3} d x

e^{x + 3} = e^{3} e^{x}

= \int e^{3} e^{x} d x

Take the constant out:

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

= e^{3} \cdot \int e^{x} d x

Use the common integral:

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

= e^{3} e^{x}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{3} e^{x} = e^{3 + x}

= e^{3 + x}

Add a constant to the solution

= e^{3 + x} + C

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