\(\int (6+6 e^2+6 x-3 \log ^2(3)) \, dx\) [7720]

Optimal result

Integrand size = 16, antiderivative size = 20 \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=1+3 x \left (2 \left (1+e^2\right )+x-\log ^2(3)\right ) \]

[Out]

1-x*(-3*x+3*ln(3)^2-6*exp(2)-6)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=3 x^2+3 x \left (2+2 e^2-\log ^2(3)\right ) \]

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=6 x+6 e^2 x+3 x^2-3 x \log ^2(3) \]

[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

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85

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

[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)

Fricas [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=-3 \, x \log \left (3\right )^{2} + 3 \, x^{2} + 6 \, x e^{2} + 6 \, x \]

[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

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=3 x^{2} + x \left (- 3 \log {\left (3 \right )}^{2} + 6 + 6 e^{2}\right ) \]

[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))

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=-3 \, x \log \left (3\right )^{2} + 3 \, x^{2} + 6 \, x e^{2} + 6 \, x \]

[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

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=-3 \, x \log \left (3\right )^{2} + 3 \, x^{2} + 6 \, x e^{2} + 6 \, x \]

[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

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \left (6+6 e^2+6 x-3 \log ^2(3)\right ) \, dx=3\,x\,\left (x+2\,{\mathrm {e}}^2-{\ln \left (3\right )}^2+2\right ) \]

[In]

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

[Out]

3*x*(x + 2*exp(2) - log(3)^2 + 2)