3.8.89 \(\int \frac {1}{16} (96 x-3 x^2) \, dx\)

Optimal. Leaf size=23 \[ 3-e^{2 e^2}+3 x^2-\frac {x^3}{16} \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.57, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12} \begin {gather*} 3 x^2-\frac {x^3}{16} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(96*x - 3*x^2)/16,x]

[Out]

3*x^2 - x^3/16

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \left (96 x-3 x^2\right ) \, dx\\ &=3 x^2-\frac {x^3}{16}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.74 \begin {gather*} -\frac {3}{16} \left (-16 x^2+\frac {x^3}{3}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(96*x - 3*x^2)/16,x]

[Out]

(-3*(-16*x^2 + x^3/3))/16

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fricas [A]  time = 0.83, size = 11, normalized size = 0.48 \begin {gather*} -\frac {1}{16} \, x^{3} + 3 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/16*x^2+6*x,x, algorithm="fricas")

[Out]

-1/16*x^3 + 3*x^2

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giac [A]  time = 0.23, size = 11, normalized size = 0.48 \begin {gather*} -\frac {1}{16} \, x^{3} + 3 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/16*x^2+6*x,x, algorithm="giac")

[Out]

-1/16*x^3 + 3*x^2

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maple [A]  time = 0.01, size = 9, normalized size = 0.39

method	result	size
gosper	\(-\frac {x^{2} \left (x -48\right )}{16}\)	\(9\)
default	\(-\frac {1}{16} x^{3}+3 x^{2}\)	\(12\)
norman	\(-\frac {1}{16} x^{3}+3 x^{2}\)	\(12\)
risch	\(-\frac {1}{16} x^{3}+3 x^{2}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/16*x^2+6*x,x,method=_RETURNVERBOSE)

[Out]

-1/16*x^2*(x-48)

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maxima [A]  time = 0.50, size = 11, normalized size = 0.48 \begin {gather*} -\frac {1}{16} \, x^{3} + 3 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/16*x^2+6*x,x, algorithm="maxima")

[Out]

-1/16*x^3 + 3*x^2

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mupad [B]  time = 0.02, size = 8, normalized size = 0.35 \begin {gather*} -\frac {x^2\,\left (x-48\right )}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x - (3*x^2)/16,x)

[Out]

-(x^2*(x - 48))/16

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sympy [A]  time = 0.05, size = 8, normalized size = 0.35 \begin {gather*} - \frac {x^{3}}{16} + 3 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/16*x**2+6*x,x)

[Out]

-x**3/16 + 3*x**2

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