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Popular >

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

Solution

\int e^{x + 2} d x

Solution

2 (e^{x + 2} x + 2 - e^{x + 2}) + C

Solution steps

\int e^{x + 2} d x

Apply u-substitution

: \int e^{u} \cdot 2 u d u

= \int 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 e^{u} u d u

Apply Integration By Parts

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

= 2 (e^{u} u - \int e^{u} d u)

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

= 2 (e^{u} u - e^{u})

Substitute back

u = x + 2

= 2 (e^{x + 2} x + 2 - e^{x + 2})

Add a constant to the solution

= 2 (e^{x + 2} x + 2 - e^{x + 2}) + C

Graph

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Frequently Asked Questions (FAQ)

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