What is the integral of 5xsqrt(x) ?

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

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integral of 5xsqrt(x)

\int 5 x x d x

2 x^{\frac{5}{2}} + C

Solution steps

\int 5 x x d x

Take the constant out:

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

= 5 \cdot \int x x d x

Simplify

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

= 5 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

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

Simplify

5 \cdot \frac{2}{5} x^{\frac{5}{2}} : 2 x^{\frac{5}{2}}

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

Add a constant to the solution

= 2 x^{\frac{5}{2}} + C