3.78.20 \(\int (6+6 e^2+6 x-3 \log ^2(3)) \, dx\)

Optimal. Leaf size=20 \[ 1+3 x \left (2 \left (1+e^2\right )+x-\log ^2(3)\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 1, number of rules used = 0, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 3 x^2+3 x \left (2+2 e^2-\log ^2(3)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[6 + 6*E^2 + 6*x - 3*Log[3]^2,x]

[Out]

3*x^2 + 3*x*(2 + 2*E^2 - Log[3]^2)

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 22, normalized size = 1.10 \begin {gather*} 6 x+6 e^2 x+3 x^2-3 x \log ^2(3) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[6 + 6*E^2 + 6*x - 3*Log[3]^2,x]

[Out]

6*x + 6*E^2*x + 3*x^2 - 3*x*Log[3]^2

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fricas [A]  time = 0.43, size = 21, normalized size = 1.05 \begin {gather*} -3 \, x \log \relax (3)^{2} + 3 \, x^{2} + 6 \, x e^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*log(3)^2+6*exp(2)+6*x+6,x, algorithm="fricas")

[Out]

-3*x*log(3)^2 + 3*x^2 + 6*x*e^2 + 6*x

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giac [A]  time = 0.12, size = 21, normalized size = 1.05 \begin {gather*} -3 \, x \log \relax (3)^{2} + 3 \, x^{2} + 6 \, x e^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*log(3)^2+6*exp(2)+6*x+6,x, algorithm="giac")

[Out]

-3*x*log(3)^2 + 3*x^2 + 6*x*e^2 + 6*x

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maple [A]  time = 0.02, size = 17, normalized size = 0.85

method	result	size
gosper	\(3 x \left (-\ln \relax (3)^{2}+2 \,{\mathrm e}^{2}+x +2\right )\)	\(17\)
norman	\(\left (-3 \ln \relax (3)^{2}+6 \,{\mathrm e}^{2}+6\right ) x +3 x^{2}\)	\(21\)
default	\(-3 x \ln \relax (3)^{2}+6 \,{\mathrm e}^{2} x +3 x^{2}+6 x\)	\(22\)
risch	\(-3 x \ln \relax (3)^{2}+6 \,{\mathrm e}^{2} x +3 x^{2}+6 x\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*ln(3)^2+6*exp(2)+6*x+6,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.36, size = 21, normalized size = 1.05 \begin {gather*} -3 \, x \log \relax (3)^{2} + 3 \, x^{2} + 6 \, x e^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*log(3)^2+6*exp(2)+6*x+6,x, algorithm="maxima")

[Out]

-3*x*log(3)^2 + 3*x^2 + 6*x*e^2 + 6*x

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mupad [B]  time = 0.07, size = 16, normalized size = 0.80 \begin {gather*} 3\,x\,\left (x+2\,{\mathrm {e}}^2-{\ln \relax (3)}^2+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x + 6*exp(2) - 3*log(3)^2 + 6,x)

[Out]

3*x*(x + 2*exp(2) - log(3)^2 + 2)

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sympy [A]  time = 0.07, size = 19, normalized size = 0.95 \begin {gather*} 3 x^{2} + x \left (- 3 \log {\relax (3 )}^{2} + 6 + 6 e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*ln(3)**2+6*exp(2)+6*x+6,x)

[Out]

3*x**2 + x*(-3*log(3)**2 + 6 + 6*exp(2))

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