What is the integral of (4+x)^{1/2} ?

The integral of (4+x)^{1/2} is 2/3 (4+x)^{3/2}+C

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integral of (4+x)^{1/2}

integral

(4 + x)^{\frac{1}{2}}

\frac{2}{3} (4 + x)^{\frac{3}{2}} + C

Solution steps

\int (4 + x)^{\frac{1}{2}} d x

Apply u-substitution

: \int u^{\frac{1}{2}} d u

= \int u^{\frac{1}{2}} d u

Apply the Power Rule

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

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

Substitute back

u = 4 + x

= \frac{2}{3} (4 + x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (4 + x)^{\frac{3}{2}} + C

x^{2} + 2 x + 3

\frac{s}{( s ^{2} + 1 )}

x^{1}

\frac{x ^{4}}{( x ^{3} + 1 )}

\frac{x}{3}

What is the integral of (4+x)^{1/2} ?
The integral of (4+x)^{1/2} is 2/3 (4+x)^{3/2}+C