What is the integral from 1 to 3 of e^{x+2} ?

The integral from 1 to 3 of e^{x+2} is e^5-e^3

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integral from 1 to 3 of e^{x+2}

\int_{1}^{3} e^{x + 2} d x

e^{5} - e^{3}

Solution steps

\int_{1}^{3} e^{x + 2} d x

e^{x + 2} = e^{2} e^{x}

= \int_{1}^{3} e^{2} e^{x} d x

Take the constant out:

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

= e^{2} \cdot \int_{1}^{3} e^{x} d x

Use the common integral:

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

= e^{2} [e^{x}]_{1}^{3}

Compute the boundaries:

e^{3} - e

= e^{2} (e^{3} - e)

Simplify

= e^{5} - e^{3}

\frac{\partial}{\partial t} (6 q (r, t)^{2} + 7 r^{3} - \frac{8}{t} - q (r, t) t)

n = 0 \sum \infty \frac{2}{n ^{2} + 6 n + 8}

(2 x - 5)^{2}

\int - \frac{16}{x ^{17}} d x

n = 1 \sum \infty \frac{6 ^{n}}{5 ^{n}}

What is the integral from 1 to 3 of e^{x+2} ?
The integral from 1 to 3 of e^{x+2} is e^5-e^3