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Popular >

integral of sqrt(x/4)

Solution

\int \frac{x}{4} d x

Solution

\frac{1}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{x}{4} d x

Simplify

\frac{x}{4} : \frac{x}{4}

= \int \frac{x}{4} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int x d x

4 = 2

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

Apply the Power Rule

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

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

Simplify

\frac{1}{2} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{1}{3} x^{\frac{3}{2}}

= \frac{1}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} x^{\frac{3}{2}} + C

Popular Examples

integral of (t+1)/(t^3)

\int \frac{t + 1}{t ^{3}} d t

integral of (2(ln(x))^2)/x

\int \frac{2 ( ln ( x ) ) ^{2}}{x} d x

integral of \sqrt[5]{1-3x}

integral of (4x+7)^2

\int (4 x + 7)^{2} d x

integral of (x^2+1)/(sqrt(x^3+3x+4))

\int \frac{x ^{2} + 1}{x ^{3} + 3 x + 4} d x

Frequently Asked Questions (FAQ)

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