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

The integral of x*x^{1/2} is 2/5 x^{5/2}+C

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integral of x*x^{1/2}

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

\frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

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

Simplify

x x^{\frac{1}{2}} : x^{\frac{3}{2}}

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

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} + C

x \to 0 lim ((x^{2}) \cdot ln (x))

y^{^{'}} + \frac{1}{x} y = 0

f (x) = 3 x^{3} - 3 x^{2} + 7, (2, 19)

\frac{d}{d x} (3^{x} lo g_{5} (x))

\int_{0}^{x} \frac{1}{1 - x} d x