What is the integral of 12x^3sqrt(x) ?

The integral of 12x^3sqrt(x) is 8/3 x^{9/2}+C

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integral of 12x^3sqrt(x)

\int 12 x^{3} x d x

\frac{8}{3} x^{\frac{9}{2}} + C

Solution steps

\int 12 x^{3} x d x

Take the constant out:

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

= 12 \cdot \int x^{3} x d x

Simplify

x^{3} x : x^{\frac{7}{2}}

= 12 \cdot \int x^{\frac{7}{2}} d x

Apply the Power Rule

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

= 12 \cdot \frac{2}{9} x^{\frac{9}{2}}

Simplify

12 \cdot \frac{2}{9} x^{\frac{9}{2}} : \frac{8}{3} x^{\frac{9}{2}}

= \frac{8}{3} x^{\frac{9}{2}}

Add a constant to the solution

= \frac{8}{3} x^{\frac{9}{2}} + C

arctan (9 x^{4})

y^{^{'}} - y - e^{3 x} = 0

f (x) = 9 x^{2} - 2 x

f (x) = 7 x + 6

\frac{d}{d x} (5 cos (4 x))

What is the integral of 12x^3sqrt(x) ?
The integral of 12x^3sqrt(x) is 8/3 x^{9/2}+C