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

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

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integral of (x^{1/2})

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

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

Solution steps

\int x^{\frac{1}{2}} d x

Apply the Power Rule

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

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

Add a constant to the solution

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

\frac{d y}{d x} + 5 y = 20

y^{^{''}} + y = cot^{2} (x)

\frac{( s + 4 )}{( s ^{2} - 2 s + 4 )}

(- 16 x y^{2} + 3 y) + (- 16 x^{2} y + 3 x) y^{^{'}} = 0

x^{2} + x y + 2 y^{2} = 18, (3, - 3)