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

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

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integral of sqrt(2+x)

\int 2 + x d x

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

Solution steps

\int 2 + x 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 = 2 + x

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{25 - x ^{2}}{16 x})

\frac{\partial ^{2}}{\partial x \partial y} (1 + x y^{2})

\int_{2}^{11} (x - 3)^{- \frac{2}{3}} d x

f (x) = arcsin (3 x)

∣ sin (x) ∣

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