What is the integral of 7sqrt(x^5) ?

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

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integral of 7sqrt(x^5)

\int 7 x^{5} d x

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

Solution steps

\int 7 x^{5} d x

Take the constant out:

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

= 7 \cdot \int x^{5} d x

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

assuming

x \geq 0

= 7 \cdot \int x^{\frac{5}{2}} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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