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

The integral of (5x^5)/(sqrt(x)) is 10/11 x^{11/2}+C

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integral of (5x^5)/(sqrt(x))

\int \frac{5 x ^{5}}{x} d x

\frac{10}{11} x^{\frac{11}{2}} + C

Solution steps

\int \frac{5 x ^{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 \frac{x ^{5}}{x} d x

Simplify

\frac{x ^{5}}{x} : x^{\frac{9}{2}}

= 5 \cdot \int x^{\frac{9}{2}} d x

Apply the Power Rule

: \frac{2}{11} x^{\frac{11}{2}}

= 5 \cdot \frac{2}{11} x^{\frac{11}{2}}

Simplify

5 \cdot \frac{2}{11} x^{\frac{11}{2}} : \frac{10}{11} x^{\frac{11}{2}}

= \frac{10}{11} x^{\frac{11}{2}}

Add a constant to the solution

= \frac{10}{11} x^{\frac{11}{2}} + C

\int x^{2} + 6 x + 5 d x

\frac{d y}{d x} = 3 y + x^{2} + 2

\int \frac{- 1}{x - 1} d x

f (x) = - 4

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)} (x + c))

What is the integral of (5x^5)/(sqrt(x)) ?
The integral of (5x^5)/(sqrt(x)) is 10/11 x^{11/2}+C