3.21.3 \(\int (3072+1536 x+21504 \log (\log (4))) \, dx\)

Optimal. Leaf size=15 \[ 12 (16+8 (x+14 \log (\log (4))))^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.07, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 768 x^2+3072 x (1+7 \log (\log (4))) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3072 + 1536*x + 21504*Log[Log[4]],x]

[Out]

768*x^2 + 3072*x*(1 + 7*Log[Log[4]])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=768 x^2+3072 x (1+7 \log (\log (4)))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} 3072 x+768 x^2+21504 x \log (\log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3072 + 1536*x + 21504*Log[Log[4]],x]

[Out]

3072*x + 768*x^2 + 21504*x*Log[Log[4]]

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fricas [A]  time = 0.53, size = 17, normalized size = 1.13 \begin {gather*} 768 \, x^{2} + 21504 \, x \log \left (2 \, \log \relax (2)\right ) + 3072 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(21504*log(2*log(2))+1536*x+3072,x, algorithm="fricas")

[Out]

768*x^2 + 21504*x*log(2*log(2)) + 3072*x

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giac [A]  time = 0.23, size = 17, normalized size = 1.13 \begin {gather*} 768 \, x^{2} + 21504 \, x \log \left (2 \, \log \relax (2)\right ) + 3072 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(21504*log(2*log(2))+1536*x+3072,x, algorithm="giac")

[Out]

768*x^2 + 21504*x*log(2*log(2)) + 3072*x

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maple [A]  time = 0.03, size = 14, normalized size = 0.93

method	result	size
gosper	\(768 x \left (x +28 \ln \left (2 \ln \relax (2)\right )+4\right )\)	\(14\)
default	\(21504 x \ln \left (2 \ln \relax (2)\right )+768 x^{2}+3072 x\)	\(18\)
norman	\(\left (21504 \ln \relax (2)+21504 \ln \left (\ln \relax (2)\right )+3072\right ) x +768 x^{2}\)	\(20\)
risch	\(21504 x \ln \left (\ln \relax (2)\right )+21504 x \ln \relax (2)+768 x^{2}+3072 x\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(21504*ln(2*ln(2))+1536*x+3072,x,method=_RETURNVERBOSE)

[Out]

768*x*(x+28*ln(2*ln(2))+4)

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maxima [A]  time = 0.41, size = 17, normalized size = 1.13 \begin {gather*} 768 \, x^{2} + 21504 \, x \log \left (2 \, \log \relax (2)\right ) + 3072 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(21504*log(2*log(2))+1536*x+3072,x, algorithm="maxima")

[Out]

768*x^2 + 21504*x*log(2*log(2)) + 3072*x

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mupad [B]  time = 0.04, size = 11, normalized size = 0.73 \begin {gather*} 768\,x\,\left (x+\ln \left ({\ln \relax (4)}^{28}\right )+4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1536*x + 21504*log(2*log(2)) + 3072,x)

[Out]

768*x*(x + log(log(4)^28) + 4)

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sympy [A]  time = 0.06, size = 19, normalized size = 1.27 \begin {gather*} 768 x^{2} + x \left (21504 \log {\left (\log {\relax (2 )} \right )} + 3072 + 21504 \log {\relax (2 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(21504*ln(2*ln(2))+1536*x+3072,x)

[Out]

768*x**2 + x*(21504*log(log(2)) + 3072 + 21504*log(2))

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