What is the integral of 8sqrt(x) ?

The integral of 8sqrt(x) is 16/3 x^{3/2}+C

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integral of 8sqrt(x)

\int 8 x d x

\frac{16}{3} x^{\frac{3}{2}} + C

Solution steps

\int 8 x d x

Take the constant out:

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

= 8 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

8 \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{16}{3} x^{\frac{3}{2}}

= \frac{16}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{16}{3} x^{\frac{3}{2}} + C

\frac{d}{d x} (\frac{3 x ^{2} + 4 x - 2}{x})

\frac{5}{x}

\int \frac{x}{a ^{2} + x ^{2}} d x

\frac{d}{d x} (x y + 8)

h \to 0 lim (4 h - h^{2})