3.10.57 \(\int (-12+32 x+4 \log (4 e)) \, dx\)

Optimal. Leaf size=14 \[ 2+4 x (-3+4 x+\log (4 e)) \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.07, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 16 x^2-4 x (2-\log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-12 + 32*x + 4*Log[4*E],x]

[Out]

16*x^2 - 4*x*(2 - Log[4])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=16 x^2-4 x (2-\log (4))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.14 \begin {gather*} -12 x+16 x^2+4 x \log (4 e) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-12 + 32*x + 4*Log[4*E],x]

[Out]

-12*x + 16*x^2 + 4*x*Log[4*E]

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fricas [A]  time = 0.63, size = 14, normalized size = 1.00 \begin {gather*} 16 \, x^{2} + 8 \, x \log \relax (2) - 8 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(4*exp(1))+32*x-12,x, algorithm="fricas")

[Out]

16*x^2 + 8*x*log(2) - 8*x

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giac [A]  time = 0.48, size = 17, normalized size = 1.21 \begin {gather*} 16 \, x^{2} + 4 \, x \log \left (4 \, e\right ) - 12 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(4*exp(1))+32*x-12,x, algorithm="giac")

[Out]

16*x^2 + 4*x*log(4*e) - 12*x

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maple [A]  time = 0.02, size = 14, normalized size = 1.00

method	result	size
gosper	\(4 x \left (-3+\ln \left (4 \,{\mathrm e}\right )+4 x \right )\)	\(14\)
norman	\(\left (-8+8 \ln \relax (2)\right ) x +16 x^{2}\)	\(15\)
risch	\(8 x \ln \relax (2)+16 x^{2}-8 x\)	\(15\)
default	\(4 \ln \left (4 \,{\mathrm e}\right ) x +16 x^{2}-12 x\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*ln(4*exp(1))+32*x-12,x,method=_RETURNVERBOSE)

[Out]

4*x*(-3+ln(4*exp(1))+4*x)

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maxima [A]  time = 0.61, size = 17, normalized size = 1.21 \begin {gather*} 16 \, x^{2} + 4 \, x \log \left (4 \, e\right ) - 12 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(4*exp(1))+32*x-12,x, algorithm="maxima")

[Out]

16*x^2 + 4*x*log(4*e) - 12*x

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mupad [B]  time = 0.04, size = 12, normalized size = 0.86 \begin {gather*} 16\,x^2+\left (\ln \left (256\right )-8\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x + 4*log(4*exp(1)) - 12,x)

[Out]

x*(log(256) - 8) + 16*x^2

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sympy [A]  time = 0.05, size = 12, normalized size = 0.86 \begin {gather*} 16 x^{2} + x \left (-8 + 8 \log {\relax (2 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*ln(4*exp(1))+32*x-12,x)

[Out]

16*x**2 + x*(-8 + 8*log(2))

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