3.86.34 \(\int (514-342 x+e^{24} (-27+18 x)+(27-18 x) \log (\log (3))) \, dx\)

Optimal. Leaf size=20 \[ x+9 (3-x) x \left (19-e^{24}+\log (\log (3))\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.85, number of steps used = 1, number of rules used = 0, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -171 x^2+\frac {9}{4} e^{24} (3-2 x)^2+514 x-\frac {9}{4} (3-2 x)^2 \log (\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[514 - 342*x + E^24*(-27 + 18*x) + (27 - 18*x)*Log[Log[3]],x]

[Out]

(9*E^24*(3 - 2*x)^2)/4 + 514*x - 171*x^2 - (9*(3 - 2*x)^2*Log[Log[3]])/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {9}{4} e^{24} (3-2 x)^2+514 x-171 x^2-\frac {9}{4} (3-2 x)^2 \log (\log (3))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 34, normalized size = 1.70 \begin {gather*} 514 x-27 e^{24} x+9 e^{24} x^2+27 x \log (\log (3))-9 x^2 (19+\log (\log (3))) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[514 - 342*x + E^24*(-27 + 18*x) + (27 - 18*x)*Log[Log[3]],x]

[Out]

514*x - 27*E^24*x + 9*E^24*x^2 + 27*x*Log[Log[3]] - 9*x^2*(19 + Log[Log[3]])

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fricas [A]  time = 0.80, size = 32, normalized size = 1.60 \begin {gather*} -171 \, x^{2} + 9 \, {\left (x^{2} - 3 \, x\right )} e^{24} - 9 \, {\left (x^{2} - 3 \, x\right )} \log \left (\log \relax (3)\right ) + 514 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x+27)*log(log(3))+(18*x-27)*exp(24)-342*x+514,x, algorithm="fricas")

[Out]

-171*x^2 + 9*(x^2 - 3*x)*e^24 - 9*(x^2 - 3*x)*log(log(3)) + 514*x

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giac [A]  time = 0.16, size = 32, normalized size = 1.60 \begin {gather*} -171 \, x^{2} + 9 \, {\left (x^{2} - 3 \, x\right )} e^{24} - 9 \, {\left (x^{2} - 3 \, x\right )} \log \left (\log \relax (3)\right ) + 514 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x+27)*log(log(3))+(18*x-27)*exp(24)-342*x+514,x, algorithm="giac")

[Out]

-171*x^2 + 9*(x^2 - 3*x)*e^24 - 9*(x^2 - 3*x)*log(log(3)) + 514*x

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maple [A]  time = 0.04, size = 28, normalized size = 1.40

method	result	size
gosper	\(x \left (9 x \,{\mathrm e}^{24}-9 \ln \left (\ln \relax (3)\right ) x -27 \,{\mathrm e}^{24}+27 \ln \left (\ln \relax (3)\right )-171 x +514\right )\)	\(28\)
norman	\(\left (-9 \ln \left (\ln \relax (3)\right )+9 \,{\mathrm e}^{24}-171\right ) x^{2}+\left (-27 \,{\mathrm e}^{24}+27 \ln \left (\ln \relax (3)\right )+514\right ) x\)	\(30\)
default	\(\ln \left (\ln \relax (3)\right ) \left (-9 x^{2}+27 x \right )+{\mathrm e}^{24} \left (9 x^{2}-27 x \right )-171 x^{2}+514 x\)	\(35\)
risch	\(-9 x^{2} \ln \left (\ln \relax (3)\right )+27 \ln \left (\ln \relax (3)\right ) x +9 x^{2} {\mathrm e}^{24}-27 x \,{\mathrm e}^{24}-171 x^{2}+514 x\)	\(36\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-18*x+27)*ln(ln(3))+(18*x-27)*exp(24)-342*x+514,x,method=_RETURNVERBOSE)

[Out]

x*(9*x*exp(24)-9*ln(ln(3))*x-27*exp(24)+27*ln(ln(3))-171*x+514)

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maxima [A]  time = 0.36, size = 32, normalized size = 1.60 \begin {gather*} -171 \, x^{2} + 9 \, {\left (x^{2} - 3 \, x\right )} e^{24} - 9 \, {\left (x^{2} - 3 \, x\right )} \log \left (\log \relax (3)\right ) + 514 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x+27)*log(log(3))+(18*x-27)*exp(24)-342*x+514,x, algorithm="maxima")

[Out]

-171*x^2 + 9*(x^2 - 3*x)*e^24 - 9*(x^2 - 3*x)*log(log(3)) + 514*x

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mupad [B]  time = 0.05, size = 30, normalized size = 1.50 \begin {gather*} x\,\left (27\,\ln \left (\ln \relax (3)\right )-27\,{\mathrm {e}}^{24}+514\right )-x^2\,\left (9\,\ln \left (\ln \relax (3)\right )-9\,{\mathrm {e}}^{24}+171\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(24)*(18*x - 27) - log(log(3))*(18*x - 27) - 342*x + 514,x)

[Out]

x*(27*log(log(3)) - 27*exp(24) + 514) - x^2*(9*log(log(3)) - 9*exp(24) + 171)

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sympy [A]  time = 0.10, size = 31, normalized size = 1.55 \begin {gather*} x^{2} \left (-171 - 9 \log {\left (\log {\relax (3 )} \right )} + 9 e^{24}\right ) + x \left (- 27 e^{24} + 27 \log {\left (\log {\relax (3 )} \right )} + 514\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-18*x+27)*ln(ln(3))+(18*x-27)*exp(24)-342*x+514,x)

[Out]

x**2*(-171 - 9*log(log(3)) + 9*exp(24)) + x*(-27*exp(24) + 27*log(log(3)) + 514)

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