What is the integral from 0 to a of 5e^x ?

The integral from 0 to a of 5e^x is 5(e^a-1)

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integral from 0 to a of 5e^x

\int_{0}^{a} 5 e^{x} d x

5 (e^{a} - 1)

Solution steps

\int_{0}^{a} 5 e^{x} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{a} e^{x} d x

Use the common integral:

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

= 5 [e^{x}]_{0}^{a}

Compute the boundaries:

e^{a} - 1

= 5 (e^{a} - 1)

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What is the integral from 0 to a of 5e^x ?
The integral from 0 to a of 5e^x is 5(e^a-1)