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

The integral of e^{sqrt(2x+4)} is e^{sqrt(2x+4)}sqrt(2x+4)-e^{sqrt(2x+4)}+C

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integral of e^{sqrt(2x+4)}

\int e^{2 x + 4} d x

e^{2 x + 4} 2 x + 4 - e^{2 x + 4} + C

Solution steps

\int e^{2 x + 4} d x

Apply u-substitution

= \int e^{u} u d u

Apply Integration By Parts

= 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 + 4

= e^{2 x + 4} 2 x + 4 - e^{2 x + 4}

Add a constant to the solution

= e^{2 x + 4} 2 x + 4 - e^{2 x + 4} + C

What is the integral of e^{sqrt(2x+4)} ?
The integral of e^{sqrt(2x+4)} is e^{sqrt(2x+4)}sqrt(2x+4)-e^{sqrt(2x+4)}+C