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

y = - 5 - 8 x^{2}, (5, - 205)

\frac{2}{1 - x}, 0

\frac{1}{1 + x ^{2}}, 0

\int_{0}^{1} x^{2} (2 x^{3} - 1)^{4} d x

\frac{d}{d x} (9 e^{2 x})