What is the integral of (sqrt(x))^9 ?

The integral of (sqrt(x))^9 is 2/11 x^{11/2}+C

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integral of (sqrt(x))^9

\int (x)^{9} d x

\frac{2}{11} x^{\frac{11}{2}} + C

Solution steps

\int (x)^{9} d x

Apply exponent rule:

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

(x)^{9} = x^{\frac{9}{2}}

= \int x^{\frac{9}{2}} d x

Apply the Power Rule

: \frac{2}{11} x^{\frac{11}{2}}

= \frac{2}{11} x^{\frac{11}{2}}

Add a constant to the solution

= \frac{2}{11} x^{\frac{11}{2}} + C

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What is the integral of (sqrt(x))^9 ?
The integral of (sqrt(x))^9 is 2/11 x^{11/2}+C