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Popular Calculus >

integral of 3x^{1/2}

Solution

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

Solution

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

Solution steps

\int 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

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

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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

Graph

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(dx)/(dt)-3x=cos(4t)

\frac{d x}{d t} - 3 x = cos (4 t)

integral of (3x+1)(3x^2+2x)^{1/3}

\int (3 x + 1) (3 x^{2} + 2 x)^{\frac{1}{3}} d x

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Frequently Asked Questions (FAQ)

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