What is the integral of 12sqrt(x^5) ?

The integral of 12sqrt(x^5) is 24/7 x^{7/2}+C

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integral of 12sqrt(x^5)

\int 12 x^{5} d x

\frac{24}{7} x^{\frac{7}{2}} + C

Solution steps

\int 12 x^{5} d x

Take the constant out:

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

= 12 \cdot \int x^{5} d x

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

assuming

x \geq 0

= 12 \cdot \int x^{\frac{5}{2}} d x

Apply the Power Rule

: \frac{2}{7} x^{\frac{7}{2}}

= 12 \cdot \frac{2}{7} x^{\frac{7}{2}}

Simplify

12 \cdot \frac{2}{7} x^{\frac{7}{2}} : \frac{24}{7} x^{\frac{7}{2}}

= \frac{24}{7} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{24}{7} x^{\frac{7}{2}} + C

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What is the integral of 12sqrt(x^5) ?
The integral of 12sqrt(x^5) is 24/7 x^{7/2}+C