What is the integral from 0 to 4 of e^{sqrt(2x+1)} ?

The integral from 0 to 4 of e^{sqrt(2x+1)} is 2e^3

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integral from 0 to 4 of e^{sqrt(2x+1)}

\int_{0}^{4} e^{2 x + 1} d x

2 e^{3}

Decimal Notation

40.17107 \dots

Solution steps

\int_{0}^{4} 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:

2 e^{3}

= 2 e^{3}

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What is the integral from 0 to 4 of e^{sqrt(2x+1)} ?
The integral from 0 to 4 of e^{sqrt(2x+1)} is 2e^3