What is the integral from 0 to 1 of e^{sqrt(2x+1)} ?

The integral from 0 to 1 of e^{sqrt(2x+1)} is sqrt(3)e^{sqrt(3)}-e^{sqrt(3)}

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integral from 0 to 1 of e^{sqrt(2x+1)}

\int_{0}^{1} e^{2 x + 1} d x

3 e^{3} - e^{3}

Decimal

4.13772 \dots

Solution steps

\int_{0}^{1} e^{2 x + 1} d x

Apply u-substitution

: \int_{1}^{3} e^{u} u d u

= \int_{1}^{3} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{1}^{3}

= [e^{u} u - \int e^{u} d u]_{1}^{3}

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

= [e^{u} u - e^{u}]_{1}^{3}

Compute the boundaries:

3 e^{3} - e^{3}

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

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What is the integral from 0 to 1 of e^{sqrt(2x+1)} ?
The integral from 0 to 1 of e^{sqrt(2x+1)} is sqrt(3)e^{sqrt(3)}-e^{sqrt(3)}