What is the integral of 2/3 x^{1/2} ?

The integral of 2/3 x^{1/2} is 4/9 x^{3/2}+C

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integral of 2/3 x^{1/2}

\int \frac{2}{3} x^{\frac{1}{2}} d x

\frac{4}{9} x^{\frac{3}{2}} + C

Solution steps

\int \frac{2}{3} x^{\frac{1}{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{3} \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

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

Simplify

\frac{2}{3} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{4}{9} x^{\frac{3}{2}}

= \frac{4}{9} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{4}{9} x^{\frac{3}{2}} + C

y^{2} = x^{3}, x = 1

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

x \to 0 lim (\frac{1}{3 + 2 ^{\frac{1}{x}}})

(x^{2} + 1) y^{^{'}} + 3 x y = 6 x

\int sin^{3} (3 x) cos^{6} (3 x) d x

What is the integral of 2/3 x^{1/2} ?
The integral of 2/3 x^{1/2} is 4/9 x^{3/2}+C