What is the integral from 1 to 25 of e^{sqrt(x)} ?

The integral from 1 to 25 of e^{sqrt(x)} is 8e^5

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integral from 1 to 25 of e^{sqrt(x)}

\int_{1}^{25} e^{x} d x

8 e^{5}

Decimal

1187.30527 \dots

Solution steps

\int_{1}^{25} e^{x} d x

Apply u-substitution

= \int_{1}^{5} e^{u} \cdot 2 u d u

Take the constant out:

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

= 2 \cdot \int_{1}^{5} e^{u} u d u

Apply Integration By Parts

= 2 [e^{u} u - \int e^{u} d u]_{1}^{5}

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

= 2 [e^{u} u - e^{u}]_{1}^{5}

Compute the boundaries:

4 e^{5}

= 2 \cdot 4 e^{5}

Simplify

= 8 e^{5}

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What is the integral from 1 to 25 of e^{sqrt(x)} ?
The integral from 1 to 25 of e^{sqrt(x)} is 8e^5