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

The integral of e^{sqrt(2x+1)} is e^{sqrt(2x+1)}sqrt(2x+1)-e^{sqrt(2x+1)}+C

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

\int e^{2 x + 1} d x

e^{2 x + 1} 2 x + 1 - e^{2 x + 1} + C

Solution steps

\int e^{2 x + 1} d x

Apply u-substitution

: \int e^{u} u d u

= \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

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

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

= e^{u} u - e^{u}

Substitute back

u = 2 x + 1

= e^{2 x + 1} 2 x + 1 - e^{2 x + 1}

Add a constant to the solution

= e^{2 x + 1} 2 x + 1 - e^{2 x + 1} + C

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What is the integral of e^{sqrt(2x+1)} ?
The integral of e^{sqrt(2x+1)} is e^{sqrt(2x+1)}sqrt(2x+1)-e^{sqrt(2x+1)}+C