What is the integral of sqrt(x\sqrt{x\sqrt{x)}} ?

The integral of sqrt(x\sqrt{x\sqrt{x)}} is 8/15 x^{15/8}+C

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integral of sqrt(x\sqrt{x\sqrt{x)}}

\int x x x d x

\frac{8}{15} x^{\frac{15}{8}} + C

Solution steps

\int x x x d x

Apply exponent rule:

(a \cdot b)^{n} = a^{n} \cdot b^{n}

x x x = x x x

= \int x x x d x

Apply exponent rule:

(a \cdot b)^{n} = a^{n} \cdot b^{n}

x x = x x

= \int x x x d x

assuming

x \geq 0

Simplify

= \int x^{\frac{7}{8}} d x

Apply the Power Rule

: \frac{8}{15} x^{\frac{15}{8}}

= \frac{8}{15} x^{\frac{15}{8}}

Add a constant to the solution

= \frac{8}{15} x^{\frac{15}{8}} + C

f (x) = 8 (x - \frac{1}{x})^{3}, at x = 2

n = 0 \sum \infty (3 x)^{n}

y = cot (x), at x = \frac{π}{4}

\frac{d}{d x} (sin (a x^{2}))

\int t^{3} + 1 d t

What is the integral of sqrt(x\sqrt{x\sqrt{x)}} ?
The integral of sqrt(x\sqrt{x\sqrt{x)}} is 8/15 x^{15/8}+C