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

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

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integral of (sqrt(x^5))

\int (x^{5}) d x

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

Solution steps

\int x^{5} d x

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

assuming

x \geq 0

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

Apply the Power Rule

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

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

Add a constant to the solution

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

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