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

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

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

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

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

Solution steps

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

(x^{2})^{\frac{1}{2}} = (x),

assuming

x \geq 0

= \int x d x

Apply the Power Rule

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} ((2 x - 3 y)^{3})

x + 8, x = 0, y = 0

y = \frac{x + x ^{2}}{e ^{x} + 1}

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\int 2 x + 4 x^{2} - \frac{5}{2} d x