3.73.18 \(\int (-6-6 e^4+18 x) \, dx\)

Optimal. Leaf size=12 \[ \left (-1-e^4+3 x\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.17, 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*} 9 x^2-6 \left (1+e^4\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-6 - 6*E^4 + 18*x,x]

[Out]

-6*(1 + E^4)*x + 9*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-6 \left (1+e^4\right ) x+9 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.25 \begin {gather*} -6 x-6 e^4 x+9 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-6 - 6*E^4 + 18*x,x]

[Out]

-6*x - 6*E^4*x + 9*x^2

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fricas [A]  time = 0.87, size = 14, normalized size = 1.17 \begin {gather*} 9 \, x^{2} - 6 \, x e^{4} - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*exp(4)+18*x-6,x, algorithm="fricas")

[Out]

9*x^2 - 6*x*e^4 - 6*x

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giac [A]  time = 2.24, size = 14, normalized size = 1.17 \begin {gather*} 9 \, x^{2} - 6 \, x e^{4} - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*exp(4)+18*x-6,x, algorithm="giac")

[Out]

9*x^2 - 6*x*e^4 - 6*x

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maple [A]  time = 0.01, size = 13, normalized size = 1.08

method	result	size
gosper	\(-3 x \left (-3 x +2 \,{\mathrm e}^{4}+2\right )\)	\(13\)
default	\(-6 x \,{\mathrm e}^{4}+9 x^{2}-6 x\)	\(15\)
norman	\(\left (-6 \,{\mathrm e}^{4}-6\right ) x +9 x^{2}\)	\(15\)
risch	\(-6 x \,{\mathrm e}^{4}+9 x^{2}-6 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-6*exp(4)+18*x-6,x,method=_RETURNVERBOSE)

[Out]

-3*x*(-3*x+2*exp(4)+2)

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maxima [A]  time = 0.35, size = 14, normalized size = 1.17 \begin {gather*} 9 \, x^{2} - 6 \, x e^{4} - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*exp(4)+18*x-6,x, algorithm="maxima")

[Out]

9*x^2 - 6*x*e^4 - 6*x

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mupad [B]  time = 0.04, size = 12, normalized size = 1.00 \begin {gather*} -3\,x\,\left (2\,{\mathrm {e}}^4-3\,x+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(18*x - 6*exp(4) - 6,x)

[Out]

-3*x*(2*exp(4) - 3*x + 2)

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sympy [A]  time = 0.07, size = 14, normalized size = 1.17 \begin {gather*} 9 x^{2} + x \left (- 6 e^{4} - 6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*exp(4)+18*x-6,x)

[Out]

9*x**2 + x*(-6*exp(4) - 6)

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