What is the integral of sqrt(x)^7 ?

The integral of sqrt(x)^7 is 2/9 x^{9/2}+C

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integral of sqrt(x)^7

\int x^{7} d x

\frac{2}{9} x^{\frac{9}{2}} + C

Solution steps

\int (x)^{7} d x

Simplify

(x)^{7} : (x)^{6} x

= \int (x)^{6} x d x

(x)^{6} = x^{3}

= \int x^{3} x d x

Simplify

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

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

Apply the Power Rule

: \frac{2}{9} x^{\frac{9}{2}}

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

Add a constant to the solution

= \frac{2}{9} x^{\frac{9}{2}} + C

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