3.77.100 \(\int \frac {1}{5} (10-12 x^2 \log (5)) \, dx\)

Optimal. Leaf size=13 \[ x \left (2-\frac {4}{5} x^2 \log (5)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, 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*} 2 x-\frac {4}{5} x^3 \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(10 - 12*x^2*Log[5])/5,x]

[Out]

2*x - (4*x^3*Log[5])/5

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}{5} \int \left (10-12 x^2 \log (5)\right ) \, dx\\ &=2 x-\frac {4}{5} x^3 \log (5)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} 2 x-\frac {4}{5} x^3 \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10 - 12*x^2*Log[5])/5,x]

[Out]

2*x - (4*x^3*Log[5])/5

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fricas [A]  time = 0.83, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{5} \, x^{3} \log \relax (5) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/5*x^2*log(5)+2,x, algorithm="fricas")

[Out]

-4/5*x^3*log(5) + 2*x

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giac [A]  time = 0.12, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{5} \, x^{3} \log \relax (5) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/5*x^2*log(5)+2,x, algorithm="giac")

[Out]

-4/5*x^3*log(5) + 2*x

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maple [A]  time = 0.02, size = 12, normalized size = 0.92

method	result	size
default	\(-\frac {4 x^{3} \ln \relax (5)}{5}+2 x\)	\(12\)
norman	\(-\frac {4 x^{3} \ln \relax (5)}{5}+2 x\)	\(12\)
risch	\(-\frac {4 x^{3} \ln \relax (5)}{5}+2 x\)	\(12\)
gosper	\(-\frac {2 x \left (2 x^{2} \ln \relax (5)-5\right )}{5}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12/5*x^2*ln(5)+2,x,method=_RETURNVERBOSE)

[Out]

-4/5*x^3*ln(5)+2*x

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maxima [A]  time = 0.35, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{5} \, x^{3} \log \relax (5) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/5*x^2*log(5)+2,x, algorithm="maxima")

[Out]

-4/5*x^3*log(5) + 2*x

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mupad [B]  time = 0.03, size = 11, normalized size = 0.85 \begin {gather*} 2\,x-\frac {4\,x^3\,\ln \relax (5)}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2 - (12*x^2*log(5))/5,x)

[Out]

2*x - (4*x^3*log(5))/5

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sympy [A]  time = 0.05, size = 12, normalized size = 0.92 \begin {gather*} - \frac {4 x^{3} \log {\relax (5 )}}{5} + 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/5*x**2*ln(5)+2,x)

[Out]

-4*x**3*log(5)/5 + 2*x

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