3.104.27 \(\int (3+4 x+2 \log (\log (3))) \, dx\)

Optimal. Leaf size=19 \[ 16 e^4+x (3+2 x)+2 x \log (\log (3)) \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.79, 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*} 2 x^2+x (3+2 \log (\log (3))) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 + 4*x + 2*Log[Log[3]],x]

[Out]

2*x^2 + x*(3 + 2*Log[Log[3]])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 x^2+x (3+2 \log (\log (3)))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} 3 x+2 x^2+2 x \log (\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + 4*x + 2*Log[Log[3]],x]

[Out]

3*x + 2*x^2 + 2*x*Log[Log[3]]

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fricas [A]  time = 0.63, size = 15, normalized size = 0.79 \begin {gather*} 2 \, x^{2} + 2 \, x \log \left (\log \relax (3)\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(log(3))+3+4*x,x, algorithm="fricas")

[Out]

2*x^2 + 2*x*log(log(3)) + 3*x

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giac [A]  time = 0.15, size = 15, normalized size = 0.79 \begin {gather*} 2 \, x^{2} + 2 \, x \log \left (\log \relax (3)\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(log(3))+3+4*x,x, algorithm="giac")

[Out]

2*x^2 + 2*x*log(log(3)) + 3*x

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maple [A]  time = 0.02, size = 16, normalized size = 0.84

method	result	size
gosper	\(2 \ln \left (\ln \relax (3)\right ) x +2 x^{2}+3 x\)	\(16\)
default	\(2 \ln \left (\ln \relax (3)\right ) x +2 x^{2}+3 x\)	\(16\)
norman	\(2 x^{2}+\left (2 \ln \left (\ln \relax (3)\right )+3\right ) x\)	\(16\)
risch	\(2 \ln \left (\ln \relax (3)\right ) x +2 x^{2}+3 x\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*ln(ln(3))+3+4*x,x,method=_RETURNVERBOSE)

[Out]

2*ln(ln(3))*x+2*x^2+3*x

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maxima [A]  time = 0.34, size = 15, normalized size = 0.79 \begin {gather*} 2 \, x^{2} + 2 \, x \log \left (\log \relax (3)\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(log(3))+3+4*x,x, algorithm="maxima")

[Out]

2*x^2 + 2*x*log(log(3)) + 3*x

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mupad [B]  time = 7.03, size = 15, normalized size = 0.79 \begin {gather*} 2\,x^2+\left (2\,\ln \left (\ln \relax (3)\right )+3\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x + 2*log(log(3)) + 3,x)

[Out]

x*(2*log(log(3)) + 3) + 2*x^2

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sympy [A]  time = 0.05, size = 14, normalized size = 0.74 \begin {gather*} 2 x^{2} + x \left (2 \log {\left (\log {\relax (3 )} \right )} + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*ln(ln(3))+3+4*x,x)

[Out]

2*x**2 + x*(2*log(log(3)) + 3)

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