3.52.11 \(\int (-144+2 e^{30}+148 x-24 x^2) \, dx\)

Optimal. Leaf size=26 \[ -1+2 \left (2-\left (-9-e^{30}+(9-2 x)^2-x\right ) x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.81, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -8 x^3+74 x^2-2 \left (72-e^{30}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-144 + 2*E^30 + 148*x - 24*x^2,x]

[Out]

-2*(72 - E^30)*x + 74*x^2 - 8*x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-2 \left (72-e^{30}\right ) x+74 x^2-8 x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 20, normalized size = 0.77 \begin {gather*} -144 x+2 e^{30} x+74 x^2-8 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-144 + 2*E^30 + 148*x - 24*x^2,x]

[Out]

-144*x + 2*E^30*x + 74*x^2 - 8*x^3

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fricas [A]  time = 0.43, size = 19, normalized size = 0.73 \begin {gather*} -8 \, x^{3} + 74 \, x^{2} + 2 \, x e^{30} - 144 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(15)^2-24*x^2+148*x-144,x, algorithm="fricas")

[Out]

-8*x^3 + 74*x^2 + 2*x*e^30 - 144*x

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giac [A]  time = 0.19, size = 19, normalized size = 0.73 \begin {gather*} -8 \, x^{3} + 74 \, x^{2} + 2 \, x e^{30} - 144 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(15)^2-24*x^2+148*x-144,x, algorithm="giac")

[Out]

-8*x^3 + 74*x^2 + 2*x*e^30 - 144*x

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maple [A]  time = 0.03, size = 18, normalized size = 0.69

method	result	size
gosper	\(2 x \left ({\mathrm e}^{30}-4 x^{2}+37 x -72\right )\)	\(18\)
risch	\(2 x \,{\mathrm e}^{30}-8 x^{3}+74 x^{2}-144 x\)	\(20\)
default	\(2 x \,{\mathrm e}^{30}-8 x^{3}+74 x^{2}-144 x\)	\(22\)
norman	\(\left (2 \,{\mathrm e}^{30}-144\right ) x +74 x^{2}-8 x^{3}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(15)^2-24*x^2+148*x-144,x,method=_RETURNVERBOSE)

[Out]

2*x*(exp(15)^2-4*x^2+37*x-72)

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maxima [A]  time = 0.35, size = 19, normalized size = 0.73 \begin {gather*} -8 \, x^{3} + 74 \, x^{2} + 2 \, x e^{30} - 144 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(15)^2-24*x^2+148*x-144,x, algorithm="maxima")

[Out]

-8*x^3 + 74*x^2 + 2*x*e^30 - 144*x

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mupad [B]  time = 0.03, size = 15, normalized size = 0.58 \begin {gather*} 2\,x\,\left (-4\,x^2+37\,x+{\mathrm {e}}^{30}-72\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(148*x + 2*exp(30) - 24*x^2 - 144,x)

[Out]

2*x*(37*x + exp(30) - 4*x^2 - 72)

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sympy [A]  time = 0.05, size = 17, normalized size = 0.65 \begin {gather*} - 8 x^{3} + 74 x^{2} + x \left (-144 + 2 e^{30}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(15)**2-24*x**2+148*x-144,x)

[Out]

-8*x**3 + 74*x**2 + x*(-144 + 2*exp(30))

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