3.96.78 \(\int (-198 x+60 x^2-4 x^3) \, dx\)

Optimal. Leaf size=19 \[ -7+e^3+x \left (x-(10-x)^2 x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps used = 1, number of rules used = 0, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^4+20 x^3-99 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-198*x + 60*x^2 - 4*x^3,x]

[Out]

-99*x^2 + 20*x^3 - x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-99 x^2+20 x^3-x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.84 \begin {gather*} -99 x^2+20 x^3-x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-198*x + 60*x^2 - 4*x^3,x]

[Out]

-99*x^2 + 20*x^3 - x^4

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fricas [A]  time = 0.50, size = 16, normalized size = 0.84 \begin {gather*} -x^{4} + 20 \, x^{3} - 99 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3+60*x^2-198*x,x, algorithm="fricas")

[Out]

-x^4 + 20*x^3 - 99*x^2

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giac [A]  time = 0.17, size = 16, normalized size = 0.84 \begin {gather*} -x^{4} + 20 \, x^{3} - 99 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3+60*x^2-198*x,x, algorithm="giac")

[Out]

-x^4 + 20*x^3 - 99*x^2

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maple [A]  time = 0.01, size = 14, normalized size = 0.74

method	result	size
gosper	\(-x^{2} \left (x^{2}-20 x +99\right )\)	\(14\)
default	\(-x^{4}+20 x^{3}-99 x^{2}\)	\(17\)
norman	\(-x^{4}+20 x^{3}-99 x^{2}\)	\(17\)
risch	\(-x^{4}+20 x^{3}-99 x^{2}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*x^3+60*x^2-198*x,x,method=_RETURNVERBOSE)

[Out]

-x^2*(x^2-20*x+99)

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maxima [A]  time = 0.36, size = 16, normalized size = 0.84 \begin {gather*} -x^{4} + 20 \, x^{3} - 99 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3+60*x^2-198*x,x, algorithm="maxima")

[Out]

-x^4 + 20*x^3 - 99*x^2

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mupad [B]  time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} -x^2\,\left (x^2-20\,x+99\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(60*x^2 - 198*x - 4*x^3,x)

[Out]

-x^2*(x^2 - 20*x + 99)

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sympy [A]  time = 0.05, size = 12, normalized size = 0.63 \begin {gather*} - x^{4} + 20 x^{3} - 99 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x**3+60*x**2-198*x,x)

[Out]

-x**4 + 20*x**3 - 99*x**2

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