What is the integral of sqrt(x)sqrt(x^{3/2-1)} ?

The integral of sqrt(x)sqrt(x^{3/2-1)} is 4/7 x^{7/4}+C

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integral of sqrt(x)sqrt(x^{3/2-1)}

\int x x^{\frac{3}{2} - 1} d x

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

Solution steps

\int x x^{\frac{3}{2} - 1} 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 x} ((x + 6)^{\frac{2}{3}})

y^{^{''}} + 25 y = 0.5 sin (5 t), y (0) = 0, y^{^{'}} (0) = 0

x \to 3 lim (3 - x)

\frac{( 4 + h ) ^{2} - 16}{h}

h \to 0 lim (\frac{1 - cos ( 2 h )}{h})

What is the integral of sqrt(x)sqrt(x^{3/2-1)} ?
The integral of sqrt(x)sqrt(x^{3/2-1)} is 4/7 x^{7/4}+C