What is the integral of sqrt(3x^5) ?

The integral of sqrt(3x^5) is sqrt(3) 2/7 x^{7/2}+C

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integral of sqrt(3x^5)

\int 3 x^{5} d x

3 \frac{2}{7} x^{\frac{7}{2}} + C

Solution steps

\int 3 x^{5} d x

3 x^{5} = 3 x^{5}

= \int 3 x^{5} d x

Take the constant out:

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

= 3 \cdot \int x^{5} d x

x^{5} = x^{\frac{5}{2}},

assuming

x \geq 0

= 3 \cdot \int x^{\frac{5}{2}} d x

Apply the Power Rule

= 3 \frac{2}{7} x^{\frac{7}{2}}

Add a constant to the solution

= 3 \frac{2}{7} x^{\frac{7}{2}} + C

What is the integral of sqrt(3x^5) ?
The integral of sqrt(3x^5) is sqrt(3) 2/7 x^{7/2}+C