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

The integral from 0 to 1 of (x+5)e^x is 5e-4

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integral from 0 to 1 of (x+5)e^x

\int_{0}^{1} (x + 5) e^{x} d x

5 e - 4

Decimal

9.59140 \dots

Solution steps

\int_{0}^{1} (x + 5) e^{x} d x

Apply Integration By Parts

: [e^{x} (x + 5) - \int e^{x} d x]_{0}^{1}

= [e^{x} (x + 5) - \int e^{x} d x]_{0}^{1}

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

= [e^{x} (x + 5) - e^{x}]_{0}^{1}

Expand

e^{x} (x + 5) - e^{x} : e^{x} x + 4 e^{x}

= [e^{x} x + 4 e^{x}]_{0}^{1}

Compute the boundaries:

5 e - 4

= 5 e - 4

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What is the integral from 0 to 1 of (x+5)e^x ?
The integral from 0 to 1 of (x+5)e^x is 5e-4