What is the integral of (4sqrt(x)) ?

The integral of (4sqrt(x)) is 8/3 x^{3/2}+C

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integral of (4sqrt(x))

\int (4 x) d x

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

Solution steps

\int 4 x d x

Take the constant out:

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

= 4 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\frac{d y}{d t} = \frac{2 t}{1 + t ^{2}} y + \frac{2}{1 + t ^{2}}

\frac{d}{d x} (9 - 2 x)

f (x) = x^{2} - 6 x + 1, at x = 1

f (x) = \frac{1}{ln ( x )}

What is the integral of (4sqrt(x)) ?
The integral of (4sqrt(x)) is 8/3 x^{3/2}+C