What is the integral of 18x^{1/2} ?

The integral of 18x^{1/2} is 12x^{3/2}+C

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integral of 18x^{1/2}

\int 18 x^{\frac{1}{2}} d x

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

Solution steps

\int 18 x^{\frac{1}{2}} d x

Take the constant out:

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

= 18 \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

= 18 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

18 \cdot \frac{2}{3} x^{\frac{3}{2}} : 12 x^{\frac{3}{2}}

= 12 x^{\frac{3}{2}}

Add a constant to the solution

= 12 x^{\frac{3}{2}} + C

\frac{\partial}{\partial x} (- \frac{1}{( x - y ) ^{2}})

f (y) = cos (y)

\int_{0}^{5} (\frac{x}{x + 4}) d x

y^{^{'}} + y + 1 = 0

\frac{d}{d x} ((1 + x) cos (x))