What is the integral from 1 to 3 of 3e^{x+6} ?

The integral from 1 to 3 of 3e^{x+6} is 3e^9-3e^7

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integral from 1 to 3 of 3e^{x+6}

\int_{1}^{3} 3 e^{x + 6} d x

3 e^{9} - 3 e^{7}

Decimal Notation

21019.35230 \dots

Solution steps

\int_{1}^{3} 3 e^{x + 6} d x

Take the constant out:

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

= 3 \cdot \int_{1}^{3} e^{x + 6} d x

e^{x + 6} = e^{6} e^{x}

= 3 \cdot \int_{1}^{3} e^{6} e^{x} d x

Take the constant out:

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

= 3 e^{6} \cdot \int_{1}^{3} e^{x} d x

Use the common integral:

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

= 3 e^{6} [e^{x}]_{1}^{3}

Compute the boundaries:

e^{3} - e

= 3 e^{6} (e^{3} - e)

Simplify

= 3 e^{9} - 3 e^{7}

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What is the integral from 1 to 3 of 3e^{x+6} ?
The integral from 1 to 3 of 3e^{x+6} is 3e^9-3e^7