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

The integral of sqrt(x\sqrt{x)} is 4/7 x^{7/4}+C

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integral of sqrt(x\sqrt{x)}

\int x x d x

\frac{4}{7} x^{\frac{7}{4}} + C

Solution steps

\int x x d x

Apply exponent rule:

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

x x = x x

= \int x x d x

assuming

x \geq 0

Simplify

= \int x^{\frac{3}{4}} d x

Apply the Power Rule

: \frac{4}{7} x^{\frac{7}{4}}

= \frac{4}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{4}} + C

\frac{d}{d t} (a cos (2 t) + b sin (2 t))

f (x) = (25 - 0.075 x) x, at x = 100

\int \frac{4 x ^{2} - 14 x - 6}{x ^{3} - 2 x ^{2} - 3 x} d x

n = 1 \sum \infty 1 - cos (\frac{1}{n})

x \to + 1 + lim (\frac{x - 1}{x - 1})

What is the integral of sqrt(x\sqrt{x)} ?
The integral of sqrt(x\sqrt{x)} is 4/7 x^{7/4}+C