What is the integral of 9sqrt(x^7) ?

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

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integral of 9sqrt(x^7)

\int 9 x^{7} d x

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

Solution steps

\int 9 x^{7} d x

Take the constant out:

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

= 9 \cdot \int x^{7} d x

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

assuming

x \geq 0

= 9 \cdot \int x^{\frac{7}{2}} d x

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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