What is the integral of (x^2)/(2sqrt(x)) ?

The integral of (x^2)/(2sqrt(x)) is 1/5 x^{5/2}+C

Popular >

integral of (x^2)/(2sqrt(x))

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

\frac{1}{5} x^{\frac{5}{2}} + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{x ^{2}}{x} d x

Simplify

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

= \frac{1}{2} \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

\frac{1}{2} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{1}{5} x^{\frac{5}{2}}

= \frac{1}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{1}{5} x^{\frac{5}{2}} + C

\int (x^{3} + 6 x)^{5} (6 x^{2} + 12) d x

\frac{d}{d x} (\frac{a x - b}{x ^{2} - 1})

\int_{0}^{4} (4 - t) t d t

f (x) = x - \frac{4}{x}, at 0

2 y^{^{''}} + 4 y^{^{'}} = 0

What is the integral of (x^2)/(2sqrt(x)) ?
The integral of (x^2)/(2sqrt(x)) is 1/5 x^{5/2}+C