What is the integral of (x^4)/(sqrt(x)) ?

The integral of (x^4)/(sqrt(x)) is 2/9 x^{9/2}+C

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integral of (x^4)/(sqrt(x))

\int \frac{x ^{4}}{x} d x

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

Solution steps

\int \frac{x ^{4}}{x} d x

Simplify

\frac{x ^{4}}{x} : x^{\frac{7}{2}}

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

Apply the Power Rule

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

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

Add a constant to the solution

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

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What is the integral of (x^4)/(sqrt(x)) ?
The integral of (x^4)/(sqrt(x)) is 2/9 x^{9/2}+C