What is the integral of 12x^{1/2} ?

The integral of 12x^{1/2} is 8x^{3/2}+C

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integral of 12x^{1/2}

\int 12 x^{\frac{1}{2}} d x

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

Solution steps

\int 12 x^{\frac{1}{2}} d x

Take the constant out:

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

= 12 \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

Simplify

12 \cdot \frac{2}{3} x^{\frac{3}{2}} : 8 x^{\frac{3}{2}}

= 8 x^{\frac{3}{2}}

Add a constant to the solution

= 8 x^{\frac{3}{2}} + C

\frac{d}{d x} (lo g_{e} (\frac{1}{x}))

d er i v a t i v e f (x) = x^{2} + x - 3

(17 + x^{2}) y^{^{'}} - 2 x y = 0

\frac{d}{d x} (\frac{cos ( x )}{1 + x ^{2}})

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