What is the integral of (sqrt(x+2)) ?

The integral of (sqrt(x+2)) is 2/3 (x+2)^{3/2}+C

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integral of (sqrt(x+2))

\int (x + 2) d x

\frac{2}{3} (x + 2)^{\frac{3}{2}} + C

Solution steps

\int x + 2 d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x + 2

= \frac{2}{3} (x + 2)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x + 2)^{\frac{3}{2}} + C

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What is the integral of (sqrt(x+2)) ?
The integral of (sqrt(x+2)) is 2/3 (x+2)^{3/2}+C