What is the integral of x^{(3/2)} ?

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

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integral of x^{(3/2)}

\int x^{(\frac{3}{2})} d x

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

Solution steps

\int x^{\frac{3}{2}} d x

Apply the Power Rule

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

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

Add a constant to the solution

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

\frac{d}{d x} (arcsin (x) \frac{8}{π})

n = 1 \sum \infty n \cdot \frac{1}{2 ^{n}}

\int \frac{1}{x ^{2} + 8 x} d x

\int_{0}^{1} 1 - y^{2} d y

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- 3 x}