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Popular >

integral of 6x^{1/2}

Solution

\int 6 x^{\frac{1}{2}} d x

Solution

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

Solution steps

\int 6 x^{\frac{1}{2}} d x

Take the constant out:

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

= 6 \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

= 6 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

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

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

Add a constant to the solution

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

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limit as x approaches 5 of-5x^2

x \to 5 lim (- 5 x^{2})

Frequently Asked Questions (FAQ)

What is the integral of 6x^{1/2} ?
The integral of 6x^{1/2} is 4x^{3/2}+C