What is the integral of 8^3sqrt(x) ?

The integral of 8^3sqrt(x) is 1024/3 x^{3/2}+C

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integral of 8^3sqrt(x)

\int 8^{3} x d x

\frac{1024}{3} x^{\frac{3}{2}} + C

Solution steps

\int 8^{3} x d x

Take the constant out:

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

= 8^{3} \cdot \int x d x

Simplify

= 512 \cdot \int x d x

Apply the Power Rule

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

= 512 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

512 \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{1024}{3} x^{\frac{3}{2}}

= \frac{1024}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{1024}{3} x^{\frac{3}{2}} + C

y^{^{'}} - \frac{6}{x} y = \frac{y ^{5}}{x ^{7}}

\int \frac{1}{x ^{2} - 2 x + 17} d x

x \to 0 lim (ln (x^{2}))

ln (3 x^{2} + 7 y^{2})

\frac{d y}{d x} = 5 y x

What is the integral of 8^3sqrt(x) ?
The integral of 8^3sqrt(x) is 1024/3 x^{3/2}+C