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

The integral of 2x^2sqrt(x) is 4/7 x^{7/2}+C

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integral of 2x^2sqrt(x)

\int 2 x^{2} x d x

\frac{4}{7} x^{\frac{7}{2}} + C

Solution steps

\int 2 x^{2} x d x

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{2}} + C

h \to 0 lim (\frac{1 + h}{h})

\int_{0}^{π} 1

\int \frac{5 x - 1}{x ^{2} ( 2 x - 1 )} d x

\frac{s + 2}{2 s \cdot ( s + 1 )}

\frac{d ^{2}}{d x ^{2}} (x y e^{(- x + 3 y)})

What is the integral of 2x^2sqrt(x) ?
The integral of 2x^2sqrt(x) is 4/7 x^{7/2}+C