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

The integral of 5sqrt(5x) is (10sqrt(5))/3 x^{3/2}+C

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integral of 5sqrt(5x)

\int 5 5 x d x

\frac{10 5}{3} x^{\frac{3}{2}} + C

Solution steps

\int 5 5 x d x

Take the constant out:

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

= 5 \cdot \int 5 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 5 \cdot \int 5 x d x

Take the constant out:

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

= 55 \cdot \int x d x

Apply the Power Rule

= 55 \frac{2}{3} x^{\frac{3}{2}}

Simplify

55 \frac{2}{3} x^{\frac{3}{2}} : \frac{10 5}{3} x^{\frac{3}{2}}

= \frac{10 5}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{10 5}{3} x^{\frac{3}{2}} + C

What is the integral of 5sqrt(5x) ?
The integral of 5sqrt(5x) is (10sqrt(5))/3 x^{3/2}+C