3.16.15 \(\int (8+(-27-12 x+15 x^2+4 x^3) \log (\log (3))) \, dx\)

Optimal. Leaf size=32 \[ (5+x) \left (8-\left (-2-(1-x)^2+x \left (4+x-x^2\right )\right ) \log (\log (3))\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.03, number of steps used = 2, number of rules used = 0, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^4 \log (\log (3))+5 x^3 \log (\log (3))-6 x^2 \log (\log (3))+8 x-27 x \log (\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[8 + (-27 - 12*x + 15*x^2 + 4*x^3)*Log[Log[3]],x]

[Out]

8*x - 27*x*Log[Log[3]] - 6*x^2*Log[Log[3]] + 5*x^3*Log[Log[3]] + x^4*Log[Log[3]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=8 x+\log (\log (3)) \int \left (-27-12 x+15 x^2+4 x^3\right ) \, dx\\ &=8 x-27 x \log (\log (3))-6 x^2 \log (\log (3))+5 x^3 \log (\log (3))+x^4 \log (\log (3))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 33, normalized size = 1.03 \begin {gather*} 8 x-27 x \log (\log (3))-6 x^2 \log (\log (3))+5 x^3 \log (\log (3))+x^4 \log (\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[8 + (-27 - 12*x + 15*x^2 + 4*x^3)*Log[Log[3]],x]

[Out]

8*x - 27*x*Log[Log[3]] - 6*x^2*Log[Log[3]] + 5*x^3*Log[Log[3]] + x^4*Log[Log[3]]

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fricas [A]  time = 0.57, size = 25, normalized size = 0.78 \begin {gather*} {\left (x^{4} + 5 \, x^{3} - 6 \, x^{2} - 27 \, x\right )} \log \left (\log \relax (3)\right ) + 8 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3+15*x^2-12*x-27)*log(log(3))+8,x, algorithm="fricas")

[Out]

(x^4 + 5*x^3 - 6*x^2 - 27*x)*log(log(3)) + 8*x

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giac [A]  time = 0.15, size = 25, normalized size = 0.78 \begin {gather*} {\left (x^{4} + 5 \, x^{3} - 6 \, x^{2} - 27 \, x\right )} \log \left (\log \relax (3)\right ) + 8 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3+15*x^2-12*x-27)*log(log(3))+8,x, algorithm="giac")

[Out]

(x^4 + 5*x^3 - 6*x^2 - 27*x)*log(log(3)) + 8*x

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maple [A]  time = 0.02, size = 26, normalized size = 0.81

method	result	size
default	\(\ln \left (\ln \relax (3)\right ) \left (x^{4}+5 x^{3}-6 x^{2}-27 x \right )+8 x\)	\(26\)
gosper	\(x \left (x^{3} \ln \left (\ln \relax (3)\right )+5 x^{2} \ln \left (\ln \relax (3)\right )-6 \ln \left (\ln \relax (3)\right ) x -27 \ln \left (\ln \relax (3)\right )+8\right )\)	\(31\)
norman	\(\ln \left (\ln \relax (3)\right ) x^{4}+5 x^{3} \ln \left (\ln \relax (3)\right )-6 x^{2} \ln \left (\ln \relax (3)\right )+\left (-27 \ln \left (\ln \relax (3)\right )+8\right ) x\)	\(34\)
risch	\(\ln \left (\ln \relax (3)\right ) x^{4}+5 x^{3} \ln \left (\ln \relax (3)\right )-6 x^{2} \ln \left (\ln \relax (3)\right )-27 \ln \left (\ln \relax (3)\right ) x +8 x\)	\(34\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^3+15*x^2-12*x-27)*ln(ln(3))+8,x,method=_RETURNVERBOSE)

[Out]

ln(ln(3))*(x^4+5*x^3-6*x^2-27*x)+8*x

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maxima [A]  time = 0.62, size = 25, normalized size = 0.78 \begin {gather*} {\left (x^{4} + 5 \, x^{3} - 6 \, x^{2} - 27 \, x\right )} \log \left (\log \relax (3)\right ) + 8 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3+15*x^2-12*x-27)*log(log(3))+8,x, algorithm="maxima")

[Out]

(x^4 + 5*x^3 - 6*x^2 - 27*x)*log(log(3)) + 8*x

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mupad [B]  time = 0.05, size = 34, normalized size = 1.06 \begin {gather*} \ln \left (\ln \relax (3)\right )\,x^4+5\,\ln \left (\ln \relax (3)\right )\,x^3-6\,\ln \left (\ln \relax (3)\right )\,x^2+\left (8-27\,\ln \left (\ln \relax (3)\right )\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8 - log(log(3))*(12*x - 15*x^2 - 4*x^3 + 27),x)

[Out]

5*x^3*log(log(3)) - 6*x^2*log(log(3)) + x^4*log(log(3)) - x*(27*log(log(3)) - 8)

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sympy [A]  time = 0.06, size = 37, normalized size = 1.16 \begin {gather*} x^{4} \log {\left (\log {\relax (3 )} \right )} + 5 x^{3} \log {\left (\log {\relax (3 )} \right )} - 6 x^{2} \log {\left (\log {\relax (3 )} \right )} + x \left (8 - 27 \log {\left (\log {\relax (3 )} \right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**3+15*x**2-12*x-27)*ln(ln(3))+8,x)

[Out]

x**4*log(log(3)) + 5*x**3*log(log(3)) - 6*x**2*log(log(3)) + x*(8 - 27*log(log(3)))

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