3.36.6 \(\int (-60-42 x+126 x^2-84 x^3) \, dx\)

Optimal. Leaf size=27 \[ 3 \left (x-7 \left (9-e^5+3 x+(1-x)^2 x^2\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 19, normalized size of antiderivative = 0.70, 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*} -21 x^4+42 x^3-21 x^2-60 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-60 - 42*x + 126*x^2 - 84*x^3,x]

[Out]

-60*x - 21*x^2 + 42*x^3 - 21*x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-60 x-21 x^2+42 x^3-21 x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 0.70 \begin {gather*} -60 x-21 x^2+42 x^3-21 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-60 - 42*x + 126*x^2 - 84*x^3,x]

[Out]

-60*x - 21*x^2 + 42*x^3 - 21*x^4

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fricas [A]  time = 0.65, size = 19, normalized size = 0.70 \begin {gather*} -21 \, x^{4} + 42 \, x^{3} - 21 \, x^{2} - 60 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-84*x^3+126*x^2-42*x-60,x, algorithm="fricas")

[Out]

-21*x^4 + 42*x^3 - 21*x^2 - 60*x

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giac [A]  time = 0.13, size = 19, normalized size = 0.70 \begin {gather*} -21 \, x^{4} + 42 \, x^{3} - 21 \, x^{2} - 60 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-84*x^3+126*x^2-42*x-60,x, algorithm="giac")

[Out]

-21*x^4 + 42*x^3 - 21*x^2 - 60*x

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maple [A]  time = 0.01, size = 19, normalized size = 0.70

method	result	size
gosper	\(-3 x \left (7 x^{3}-14 x^{2}+7 x +20\right )\)	\(19\)
default	\(-21 x^{4}+42 x^{3}-21 x^{2}-60 x\)	\(20\)
norman	\(-21 x^{4}+42 x^{3}-21 x^{2}-60 x\)	\(20\)
risch	\(-21 x^{4}+42 x^{3}-21 x^{2}-60 x\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-84*x^3+126*x^2-42*x-60,x,method=_RETURNVERBOSE)

[Out]

-3*x*(7*x^3-14*x^2+7*x+20)

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maxima [A]  time = 0.72, size = 19, normalized size = 0.70 \begin {gather*} -21 \, x^{4} + 42 \, x^{3} - 21 \, x^{2} - 60 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-84*x^3+126*x^2-42*x-60,x, algorithm="maxima")

[Out]

-21*x^4 + 42*x^3 - 21*x^2 - 60*x

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mupad [B]  time = 0.03, size = 19, normalized size = 0.70 \begin {gather*} -21\,x^4+42\,x^3-21\,x^2-60\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(126*x^2 - 42*x - 84*x^3 - 60,x)

[Out]

42*x^3 - 21*x^2 - 60*x - 21*x^4

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sympy [A]  time = 0.05, size = 17, normalized size = 0.63 \begin {gather*} - 21 x^{4} + 42 x^{3} - 21 x^{2} - 60 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-84*x**3+126*x**2-42*x-60,x)

[Out]

-21*x**4 + 42*x**3 - 21*x**2 - 60*x

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