What is the integral of (x^3)/(sqrt(x)) ?

The integral of (x^3)/(sqrt(x)) is 2/7 x^{7/2}+C

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integral of (x^3)/(sqrt(x))

\int \frac{x ^{3}}{x} d x

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

Solution steps

\int \frac{x ^{3}}{x} d x

Simplify

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

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

Apply the Power Rule

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

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

Add a constant to the solution

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

\int x + 2 - x^{2} d x

y^{^{'}} = 9 x + y, y (0) = 4

\int_{0}^{1} \frac{13}{4 y - 1} d y

e^{- 8 x}

What is the integral of (x^3)/(sqrt(x)) ?
The integral of (x^3)/(sqrt(x)) is 2/7 x^{7/2}+C