What is the integral of sqrt(x)^{11} ?

The integral of sqrt(x)^{11} is 2/13 x^{13/2}+C

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integral of sqrt(x)^{11}

\int x^{11} d x

\frac{2}{13} x^{\frac{13}{2}} + C

Solution steps

\int (x)^{11} d x

Apply exponent rule:

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

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

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

Apply the Power Rule

: \frac{2}{13} x^{\frac{13}{2}}

= \frac{2}{13} x^{\frac{13}{2}}

Add a constant to the solution

= \frac{2}{13} x^{\frac{13}{2}} + C

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What is the integral of sqrt(x)^{11} ?
The integral of sqrt(x)^{11} is 2/13 x^{13/2}+C